scripts/A1. Stan simulations.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: zoo\n",
      "\n",
      "Warning message in library(package, lib.loc = lib.loc, character.only = TRUE, logical.return = TRUE, :\n",
      "“there is no package called ‘zoo’”\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[1] ‘2.19.3’"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[1] ‘2.21.0.1’"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "'2.21.0'"
      ],
      "text/latex": [
       "'2.21.0'"
      ],
      "text/markdown": [
       "'2.21.0'"
      ],
      "text/plain": [
       "[1] \"2.21.0\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "libraries = c(\"dplyr\",\"magrittr\",\"tidyr\",\"ggplot2\",\"rstan\",\"readxl\")\n",
    "for(x in libraries) { library(x,character.only=TRUE,warn.conflicts=FALSE,quietly=TRUE) }\n",
    "\n",
    "require(zoo)\n",
    "require(lubridate)\n",
    "\n",
    "base_sz = 12 # base_size parameter\n",
    "theme_set(theme_bw())\n",
    "\n",
    "'%&%' = function(x,y) paste0(x,y)\n",
    "\n",
    "options(mc.cores = parallel::detectCores())\n",
    "rstan_options(auto_write = TRUE)\n",
    "\n",
    "packageVersion(\"rstan\")\n",
    "packageVersion(\"StanHeaders\")\n",
    "rstan::stan_version()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 18 × 6</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>InfectorOnset</th><th scope=col>InfecteeOnset</th><th scope=col>ER</th><th scope=col>EL</th><th scope=col>SL</th><th scope=col>SR</th></tr>\n",
       "\t<tr><th scope=col>&lt;date&gt;</th><th scope=col>&lt;date&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>2020-01-17</td><td>2020-01-20</td><td>48</td><td>47</td><td>50</td><td>51</td></tr>\n",
       "\t<tr><td>2020-01-22</td><td>2020-01-26</td><td>53</td><td>52</td><td>56</td><td>57</td></tr>\n",
       "\t<tr><td>2020-01-24</td><td>2020-01-26</td><td>55</td><td>54</td><td>56</td><td>57</td></tr>\n",
       "\t<tr><td>2020-01-24</td><td>2020-01-26</td><td>55</td><td>54</td><td>56</td><td>57</td></tr>\n",
       "\t<tr><td>2020-01-26</td><td>2020-01-30</td><td>57</td><td>56</td><td>60</td><td>61</td></tr>\n",
       "\t<tr><td>2020-01-26</td><td>2020-01-29</td><td>57</td><td>56</td><td>59</td><td>60</td></tr>\n",
       "\t<tr><td>2020-01-26</td><td>2020-01-30</td><td>57</td><td>56</td><td>60</td><td>61</td></tr>\n",
       "\t<tr><td>2020-01-26</td><td>2020-01-30</td><td>57</td><td>56</td><td>60</td><td>61</td></tr>\n",
       "\t<tr><td>2020-01-21</td><td>2020-01-24</td><td>52</td><td>51</td><td>54</td><td>55</td></tr>\n",
       "\t<tr><td>2020-01-21</td><td>2020-01-24</td><td>52</td><td>51</td><td>54</td><td>55</td></tr>\n",
       "\t<tr><td>2020-01-20</td><td>2020-01-29</td><td>51</td><td>50</td><td>59</td><td>60</td></tr>\n",
       "\t<tr><td>2020-02-01</td><td>2020-02-05</td><td>63</td><td>62</td><td>66</td><td>67</td></tr>\n",
       "\t<tr><td>2019-12-20</td><td>2019-12-25</td><td>20</td><td>19</td><td>24</td><td>25</td></tr>\n",
       "\t<tr><td>2019-12-20</td><td>2019-12-29</td><td>20</td><td>19</td><td>28</td><td>29</td></tr>\n",
       "\t<tr><td>2019-12-27</td><td>2020-01-03</td><td>27</td><td>26</td><td>33</td><td>34</td></tr>\n",
       "\t<tr><td>2019-12-12</td><td>2019-12-19</td><td>12</td><td>11</td><td>18</td><td>19</td></tr>\n",
       "\t<tr><td>2019-12-21</td><td>2019-12-24</td><td>21</td><td>20</td><td>23</td><td>24</td></tr>\n",
       "\t<tr><td>2020-01-04</td><td>2020-01-11</td><td>35</td><td>34</td><td>41</td><td>42</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 18 × 6\n",
       "\\begin{tabular}{llllll}\n",
       " InfectorOnset & InfecteeOnset & ER & EL & SL & SR\\\\\n",
       " <date> & <date> & <int> & <int> & <int> & <int>\\\\\n",
       "\\hline\n",
       "\t 2020-01-17 & 2020-01-20 & 48 & 47 & 50 & 51\\\\\n",
       "\t 2020-01-22 & 2020-01-26 & 53 & 52 & 56 & 57\\\\\n",
       "\t 2020-01-24 & 2020-01-26 & 55 & 54 & 56 & 57\\\\\n",
       "\t 2020-01-24 & 2020-01-26 & 55 & 54 & 56 & 57\\\\\n",
       "\t 2020-01-26 & 2020-01-30 & 57 & 56 & 60 & 61\\\\\n",
       "\t 2020-01-26 & 2020-01-29 & 57 & 56 & 59 & 60\\\\\n",
       "\t 2020-01-26 & 2020-01-30 & 57 & 56 & 60 & 61\\\\\n",
       "\t 2020-01-26 & 2020-01-30 & 57 & 56 & 60 & 61\\\\\n",
       "\t 2020-01-21 & 2020-01-24 & 52 & 51 & 54 & 55\\\\\n",
       "\t 2020-01-21 & 2020-01-24 & 52 & 51 & 54 & 55\\\\\n",
       "\t 2020-01-20 & 2020-01-29 & 51 & 50 & 59 & 60\\\\\n",
       "\t 2020-02-01 & 2020-02-05 & 63 & 62 & 66 & 67\\\\\n",
       "\t 2019-12-20 & 2019-12-25 & 20 & 19 & 24 & 25\\\\\n",
       "\t 2019-12-20 & 2019-12-29 & 20 & 19 & 28 & 29\\\\\n",
       "\t 2019-12-27 & 2020-01-03 & 27 & 26 & 33 & 34\\\\\n",
       "\t 2019-12-12 & 2019-12-19 & 12 & 11 & 18 & 19\\\\\n",
       "\t 2019-12-21 & 2019-12-24 & 21 & 20 & 23 & 24\\\\\n",
       "\t 2020-01-04 & 2020-01-11 & 35 & 34 & 41 & 42\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 18 × 6\n",
       "\n",
       "| InfectorOnset &lt;date&gt; | InfecteeOnset &lt;date&gt; | ER &lt;int&gt; | EL &lt;int&gt; | SL &lt;int&gt; | SR &lt;int&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "| 2020-01-17 | 2020-01-20 | 48 | 47 | 50 | 51 |\n",
       "| 2020-01-22 | 2020-01-26 | 53 | 52 | 56 | 57 |\n",
       "| 2020-01-24 | 2020-01-26 | 55 | 54 | 56 | 57 |\n",
       "| 2020-01-24 | 2020-01-26 | 55 | 54 | 56 | 57 |\n",
       "| 2020-01-26 | 2020-01-30 | 57 | 56 | 60 | 61 |\n",
       "| 2020-01-26 | 2020-01-29 | 57 | 56 | 59 | 60 |\n",
       "| 2020-01-26 | 2020-01-30 | 57 | 56 | 60 | 61 |\n",
       "| 2020-01-26 | 2020-01-30 | 57 | 56 | 60 | 61 |\n",
       "| 2020-01-21 | 2020-01-24 | 52 | 51 | 54 | 55 |\n",
       "| 2020-01-21 | 2020-01-24 | 52 | 51 | 54 | 55 |\n",
       "| 2020-01-20 | 2020-01-29 | 51 | 50 | 59 | 60 |\n",
       "| 2020-02-01 | 2020-02-05 | 63 | 62 | 66 | 67 |\n",
       "| 2019-12-20 | 2019-12-25 | 20 | 19 | 24 | 25 |\n",
       "| 2019-12-20 | 2019-12-29 | 20 | 19 | 28 | 29 |\n",
       "| 2019-12-27 | 2020-01-03 | 27 | 26 | 33 | 34 |\n",
       "| 2019-12-12 | 2019-12-19 | 12 | 11 | 18 | 19 |\n",
       "| 2019-12-21 | 2019-12-24 | 21 | 20 | 23 | 24 |\n",
       "| 2020-01-04 | 2020-01-11 | 35 | 34 | 41 | 42 |\n",
       "\n"
      ],
      "text/plain": [
       "   InfectorOnset InfecteeOnset ER EL SL SR\n",
       "1  2020-01-17    2020-01-20    48 47 50 51\n",
       "2  2020-01-22    2020-01-26    53 52 56 57\n",
       "3  2020-01-24    2020-01-26    55 54 56 57\n",
       "4  2020-01-24    2020-01-26    55 54 56 57\n",
       "5  2020-01-26    2020-01-30    57 56 60 61\n",
       "6  2020-01-26    2020-01-29    57 56 59 60\n",
       "7  2020-01-26    2020-01-30    57 56 60 61\n",
       "8  2020-01-26    2020-01-30    57 56 60 61\n",
       "9  2020-01-21    2020-01-24    52 51 54 55\n",
       "10 2020-01-21    2020-01-24    52 51 54 55\n",
       "11 2020-01-20    2020-01-29    51 50 59 60\n",
       "12 2020-02-01    2020-02-05    63 62 66 67\n",
       "13 2019-12-20    2019-12-25    20 19 24 25\n",
       "14 2019-12-20    2019-12-29    20 19 28 29\n",
       "15 2019-12-27    2020-01-03    27 26 33 34\n",
       "16 2019-12-12    2019-12-19    12 11 18 19\n",
       "17 2019-12-21    2019-12-24    21 20 23 24\n",
       "18 2020-01-04    2020-01-11    35 34 41 42"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "read.csv(\"../../data/supplemetary table.csv\") %>% \n",
    "    filter(SIClassification=='Certain') %>%\n",
    "    select(-X, -Source, -SIClassification, -DiagnosisCountry) %>%\n",
    "    mutate(InfectorOnset = as.Date(InfectorOnset, format=\"%m/%d/%Y\"), \n",
    "           InfecteeOnset = as.Date(InfecteeOnset, format=\"%m/%d/%Y\")) -> df\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 18 × 8</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>InfectorOnset</th><th scope=col>InfecteeOnset</th><th scope=col>ER</th><th scope=col>EL</th><th scope=col>SL</th><th scope=col>SR</th><th scope=col>tstar</th><th scope=col>dist</th></tr>\n",
       "\t<tr><th scope=col>&lt;date&gt;</th><th scope=col>&lt;date&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>2020-01-17</td><td>2020-01-20</td><td>48</td><td>47</td><td>50</td><td>51</td><td>73</td><td>3</td></tr>\n",
       "\t<tr><td>2020-01-22</td><td>2020-01-26</td><td>53</td><td>52</td><td>56</td><td>57</td><td>73</td><td>4</td></tr>\n",
       "\t<tr><td>2020-01-24</td><td>2020-01-26</td><td>55</td><td>54</td><td>56</td><td>57</td><td>73</td><td>2</td></tr>\n",
       "\t<tr><td>2020-01-24</td><td>2020-01-26</td><td>55</td><td>54</td><td>56</td><td>57</td><td>73</td><td>2</td></tr>\n",
       "\t<tr><td>2020-01-26</td><td>2020-01-30</td><td>57</td><td>56</td><td>60</td><td>61</td><td>73</td><td>4</td></tr>\n",
       "\t<tr><td>2020-01-26</td><td>2020-01-29</td><td>57</td><td>56</td><td>59</td><td>60</td><td>73</td><td>3</td></tr>\n",
       "\t<tr><td>2020-01-26</td><td>2020-01-30</td><td>57</td><td>56</td><td>60</td><td>61</td><td>73</td><td>4</td></tr>\n",
       "\t<tr><td>2020-01-26</td><td>2020-01-30</td><td>57</td><td>56</td><td>60</td><td>61</td><td>73</td><td>4</td></tr>\n",
       "\t<tr><td>2020-01-21</td><td>2020-01-24</td><td>52</td><td>51</td><td>54</td><td>55</td><td>73</td><td>3</td></tr>\n",
       "\t<tr><td>2020-01-21</td><td>2020-01-24</td><td>52</td><td>51</td><td>54</td><td>55</td><td>73</td><td>3</td></tr>\n",
       "\t<tr><td>2020-01-20</td><td>2020-01-29</td><td>51</td><td>50</td><td>59</td><td>60</td><td>73</td><td>9</td></tr>\n",
       "\t<tr><td>2020-02-01</td><td>2020-02-05</td><td>63</td><td>62</td><td>66</td><td>67</td><td>73</td><td>4</td></tr>\n",
       "\t<tr><td>2019-12-20</td><td>2019-12-25</td><td>20</td><td>19</td><td>24</td><td>25</td><td>73</td><td>5</td></tr>\n",
       "\t<tr><td>2019-12-20</td><td>2019-12-29</td><td>20</td><td>19</td><td>28</td><td>29</td><td>73</td><td>9</td></tr>\n",
       "\t<tr><td>2019-12-27</td><td>2020-01-03</td><td>27</td><td>26</td><td>33</td><td>34</td><td>73</td><td>7</td></tr>\n",
       "\t<tr><td>2019-12-12</td><td>2019-12-19</td><td>12</td><td>11</td><td>18</td><td>19</td><td>73</td><td>7</td></tr>\n",
       "\t<tr><td>2019-12-21</td><td>2019-12-24</td><td>21</td><td>20</td><td>23</td><td>24</td><td>73</td><td>3</td></tr>\n",
       "\t<tr><td>2020-01-04</td><td>2020-01-11</td><td>35</td><td>34</td><td>41</td><td>42</td><td>73</td><td>7</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 18 × 8\n",
       "\\begin{tabular}{llllllll}\n",
       " InfectorOnset & InfecteeOnset & ER & EL & SL & SR & tstar & dist\\\\\n",
       " <date> & <date> & <int> & <int> & <int> & <int> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 2020-01-17 & 2020-01-20 & 48 & 47 & 50 & 51 & 73 & 3\\\\\n",
       "\t 2020-01-22 & 2020-01-26 & 53 & 52 & 56 & 57 & 73 & 4\\\\\n",
       "\t 2020-01-24 & 2020-01-26 & 55 & 54 & 56 & 57 & 73 & 2\\\\\n",
       "\t 2020-01-24 & 2020-01-26 & 55 & 54 & 56 & 57 & 73 & 2\\\\\n",
       "\t 2020-01-26 & 2020-01-30 & 57 & 56 & 60 & 61 & 73 & 4\\\\\n",
       "\t 2020-01-26 & 2020-01-29 & 57 & 56 & 59 & 60 & 73 & 3\\\\\n",
       "\t 2020-01-26 & 2020-01-30 & 57 & 56 & 60 & 61 & 73 & 4\\\\\n",
       "\t 2020-01-26 & 2020-01-30 & 57 & 56 & 60 & 61 & 73 & 4\\\\\n",
       "\t 2020-01-21 & 2020-01-24 & 52 & 51 & 54 & 55 & 73 & 3\\\\\n",
       "\t 2020-01-21 & 2020-01-24 & 52 & 51 & 54 & 55 & 73 & 3\\\\\n",
       "\t 2020-01-20 & 2020-01-29 & 51 & 50 & 59 & 60 & 73 & 9\\\\\n",
       "\t 2020-02-01 & 2020-02-05 & 63 & 62 & 66 & 67 & 73 & 4\\\\\n",
       "\t 2019-12-20 & 2019-12-25 & 20 & 19 & 24 & 25 & 73 & 5\\\\\n",
       "\t 2019-12-20 & 2019-12-29 & 20 & 19 & 28 & 29 & 73 & 9\\\\\n",
       "\t 2019-12-27 & 2020-01-03 & 27 & 26 & 33 & 34 & 73 & 7\\\\\n",
       "\t 2019-12-12 & 2019-12-19 & 12 & 11 & 18 & 19 & 73 & 7\\\\\n",
       "\t 2019-12-21 & 2019-12-24 & 21 & 20 & 23 & 24 & 73 & 3\\\\\n",
       "\t 2020-01-04 & 2020-01-11 & 35 & 34 & 41 & 42 & 73 & 7\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 18 × 8\n",
       "\n",
       "| InfectorOnset &lt;date&gt; | InfecteeOnset &lt;date&gt; | ER &lt;int&gt; | EL &lt;int&gt; | SL &lt;int&gt; | SR &lt;int&gt; | tstar &lt;dbl&gt; | dist &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|\n",
       "| 2020-01-17 | 2020-01-20 | 48 | 47 | 50 | 51 | 73 | 3 |\n",
       "| 2020-01-22 | 2020-01-26 | 53 | 52 | 56 | 57 | 73 | 4 |\n",
       "| 2020-01-24 | 2020-01-26 | 55 | 54 | 56 | 57 | 73 | 2 |\n",
       "| 2020-01-24 | 2020-01-26 | 55 | 54 | 56 | 57 | 73 | 2 |\n",
       "| 2020-01-26 | 2020-01-30 | 57 | 56 | 60 | 61 | 73 | 4 |\n",
       "| 2020-01-26 | 2020-01-29 | 57 | 56 | 59 | 60 | 73 | 3 |\n",
       "| 2020-01-26 | 2020-01-30 | 57 | 56 | 60 | 61 | 73 | 4 |\n",
       "| 2020-01-26 | 2020-01-30 | 57 | 56 | 60 | 61 | 73 | 4 |\n",
       "| 2020-01-21 | 2020-01-24 | 52 | 51 | 54 | 55 | 73 | 3 |\n",
       "| 2020-01-21 | 2020-01-24 | 52 | 51 | 54 | 55 | 73 | 3 |\n",
       "| 2020-01-20 | 2020-01-29 | 51 | 50 | 59 | 60 | 73 | 9 |\n",
       "| 2020-02-01 | 2020-02-05 | 63 | 62 | 66 | 67 | 73 | 4 |\n",
       "| 2019-12-20 | 2019-12-25 | 20 | 19 | 24 | 25 | 73 | 5 |\n",
       "| 2019-12-20 | 2019-12-29 | 20 | 19 | 28 | 29 | 73 | 9 |\n",
       "| 2019-12-27 | 2020-01-03 | 27 | 26 | 33 | 34 | 73 | 7 |\n",
       "| 2019-12-12 | 2019-12-19 | 12 | 11 | 18 | 19 | 73 | 7 |\n",
       "| 2019-12-21 | 2019-12-24 | 21 | 20 | 23 | 24 | 73 | 3 |\n",
       "| 2020-01-04 | 2020-01-11 | 35 | 34 | 41 | 42 | 73 | 7 |\n",
       "\n"
      ],
      "text/plain": [
       "   InfectorOnset InfecteeOnset ER EL SL SR tstar dist\n",
       "1  2020-01-17    2020-01-20    48 47 50 51 73    3   \n",
       "2  2020-01-22    2020-01-26    53 52 56 57 73    4   \n",
       "3  2020-01-24    2020-01-26    55 54 56 57 73    2   \n",
       "4  2020-01-24    2020-01-26    55 54 56 57 73    2   \n",
       "5  2020-01-26    2020-01-30    57 56 60 61 73    4   \n",
       "6  2020-01-26    2020-01-29    57 56 59 60 73    3   \n",
       "7  2020-01-26    2020-01-30    57 56 60 61 73    4   \n",
       "8  2020-01-26    2020-01-30    57 56 60 61 73    4   \n",
       "9  2020-01-21    2020-01-24    52 51 54 55 73    3   \n",
       "10 2020-01-21    2020-01-24    52 51 54 55 73    3   \n",
       "11 2020-01-20    2020-01-29    51 50 59 60 73    9   \n",
       "12 2020-02-01    2020-02-05    63 62 66 67 73    4   \n",
       "13 2019-12-20    2019-12-25    20 19 24 25 73    5   \n",
       "14 2019-12-20    2019-12-29    20 19 28 29 73    9   \n",
       "15 2019-12-27    2020-01-03    27 26 33 34 73    7   \n",
       "16 2019-12-12    2019-12-19    12 11 18 19 73    7   \n",
       "17 2019-12-21    2019-12-24    21 20 23 24 73    3   \n",
       "18 2020-01-04    2020-01-11    35 34 41 42 73    7   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "CUTOFF_TIME = as.Date('2020-02-12')\n",
    "t0 = as.Date('2019-12-01')\n",
    "\n",
    "df['tstar'] = CUTOFF_TIME\n",
    "df %<>% mutate(dist = (SR+SL)/2-(ER+EL)/2,\n",
    "               SL = if_else(SL < EL, EL, SL), \n",
    "               ER = if_else(ER > SR, SR, ER), \n",
    "               tstar = as.numeric(tstar - t0)) \n",
    "\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "4.61111111111111"
      ],
      "text/latex": [
       "4.61111111111111"
      ],
      "text/markdown": [
       "4.61111111111111"
      ],
      "text/plain": [
       "[1] 4.611111"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(df$dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.226548077152"
      ],
      "text/latex": [
       "2.226548077152"
      ],
      "text/markdown": [
       "2.226548077152"
      ],
      "text/plain": [
       "[1] 2.226548"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sd(df$dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_drname = \"../../data\"\n",
    "flname = 'data.csv'\n",
    "write.table(df, paste0(data_drname,flname), row.names=FALSE, sep=\",\", quote = FALSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stan simulations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "stanmaindir = '../../../../Hokkaido_Backup/Wuhan_Serial_interval_2020/certain'\n",
    "unlink(stanmaindir, recursive=T)\n",
    "dir.create(stanmaindir)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# No truncation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"maroon\">Lognormal distribution</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT src/cmdstan/main.o -MM -E -MG -MP -MF src/cmdstan/main.d src/cmdstan/main.cpp'</span></li><li>''</li><li>'--- Translating Stan model to C++ code ---'</li><li><span style=white-space:pre-wrap>'bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.stan'</span></li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.hpp'</span></li><li>''</li><li>'--- Compiling, linking C++ code ---'</li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.hpp'</span></li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit'</span></li><li>'Running 1'</li><li>'Running 2'</li><li>'Running 3'</li><li>'Running 4'</li><li>'Running 5'</li><li>'Running 6'</li><li>'Running 7'</li><li>'Running 8'</li><li>'Running 9'</li><li>'Running 10'</li><li>'Finished sampling haha!'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_4.1.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI   -c -MT src/cmdstan/main.o -MM -E -MG -MP -MF src/cmdstan/main.d src/cmdstan/main.cpp'\n",
       "\\item ''\n",
       "\\item '--- Translating Stan model to C++ code ---'\n",
       "\\item 'bin/stanc  --o=../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-no\\_truncation/fit.hpp ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-no\\_truncation/fit.stan'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_4.1.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI   -c -MT ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-no\\_truncation/fit.o -MT ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-no\\_truncation/fit -include ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-no\\_truncation/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-no\\_truncation/fit.d ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-no\\_truncation/fit.hpp'\n",
       "\\item ''\n",
       "\\item '--- Compiling, linking C++ code ---'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_4.1.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI   -c  -x c++ -o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-no\\_truncation/fit.o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-no\\_truncation/fit.hpp'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_4.1.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan\\_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan\\_math/lib/tbb\"  ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-no\\_truncation/fit.o src/cmdstan/main.o         stan/lib/stan\\_math/lib/sundials\\_4.1.0/lib/libsundials\\_nvecserial.a stan/lib/stan\\_math/lib/sundials\\_4.1.0/lib/libsundials\\_cvodes.a stan/lib/stan\\_math/lib/sundials\\_4.1.0/lib/libsundials\\_idas.a stan/lib/stan\\_math/lib/sundials\\_4.1.0/lib/libsundials\\_kinsol.a stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib/libboost\\_serialization.so stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib/libboost\\_mpi.so stan/lib/stan\\_math/stan/math/prim/functor/mpi\\_cluster\\_inst.o stan/lib/stan\\_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-no\\_truncation/fit'\n",
       "\\item 'Running 1'\n",
       "\\item 'Running 2'\n",
       "\\item 'Running 3'\n",
       "\\item 'Running 4'\n",
       "\\item 'Running 5'\n",
       "\\item 'Running 6'\n",
       "\\item 'Running 7'\n",
       "\\item 'Running 8'\n",
       "\\item 'Running 9'\n",
       "\\item 'Running 10'\n",
       "\\item 'Finished sampling haha!'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT src/cmdstan/main.o -MM -E -MG -MP -MF src/cmdstan/main.d src/cmdstan/main.cpp'</span>\n",
       "2. ''\n",
       "3. '--- Translating Stan model to C++ code ---'\n",
       "4. <span style=white-space:pre-wrap>'bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.stan'</span>\n",
       "5. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.hpp'</span>\n",
       "6. ''\n",
       "7. '--- Compiling, linking C++ code ---'\n",
       "8. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.hpp'</span>\n",
       "9. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit'</span>\n",
       "10. 'Running 1'\n",
       "11. 'Running 2'\n",
       "12. 'Running 3'\n",
       "13. 'Running 4'\n",
       "14. 'Running 5'\n",
       "15. 'Running 6'\n",
       "16. 'Running 7'\n",
       "17. 'Running 8'\n",
       "18. 'Running 9'\n",
       "19. 'Running 10'\n",
       "20. 'Finished sampling haha!'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT src/cmdstan/main.o -MM -E -MG -MP -MF src/cmdstan/main.d src/cmdstan/main.cpp\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           \n",
       " [2] \"\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                \n",
       " [3] \"--- Translating Stan model to C++ code ---\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      \n",
       " [4] \"bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.stan\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     \n",
       " [5] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.hpp\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \n",
       " [6] \"\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                \n",
       " [7] \"--- Compiling, linking C++ code ---\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \n",
       " [8] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.hpp\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        \n",
       " [9] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\\\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\\\" -Wl,-rpath,\\\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\\\" -Wl,-L,\\\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\\\" -Wl,-rpath,\\\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\\\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-no_truncation/fit\"\n",
       "[10] \"Running 1\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       \n",
       "[11] \"Running 2\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       \n",
       "[12] \"Running 3\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       \n",
       "[13] \"Running 4\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       \n",
       "[14] \"Running 5\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       \n",
       "[15] \"Running 6\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       \n",
       "[16] \"Running 7\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       \n",
       "[17] \"Running 8\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       \n",
       "[18] \"Running 9\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       \n",
       "[19] \"Running 10\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      \n",
       "[20] \"Finished sampling haha!\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## main dir for Stan simulations\n",
    "standirname = stanmaindir%&%\"/lognormal-no_truncation\"\n",
    "unlink(standirname, recursive=T)\n",
    "dir.create(standirname)\n",
    "\n",
    "# Dumping data\n",
    "N = nrow(df)\n",
    "E_L = df$EL\n",
    "E_R = df$ER\n",
    "S_L = df$SL\n",
    "S_R = df$SR\n",
    "stan_rdump(c('E_L', 'E_R', 'S_L', 'S_R', 'N'), file=standirname%&%\"/Data.R\") \n",
    "\n",
    "# Dumping initial conditions\n",
    "e_raw = rep(.5, N)\n",
    "s_raw = rep(.5, N)\n",
    "logmean_SI = log(mean(df$dist))\n",
    "logsd_SI = log(sd(df$dist))\n",
    "stan_rdump(c('e_raw', 's_raw', 'logmean_SI', 'logsd_SI'), file=standirname%&%\"/Init.R\") \n",
    "\n",
    "# Stan program\n",
    "\"data {\n",
    "    int<lower = 0> N; // number of records\n",
    "    vector<lower = 0>[N] E_L;\n",
    "    vector<lower = 0>[N] E_R;\n",
    "    vector<lower = 0>[N] S_L;\n",
    "    vector<lower = 0>[N] S_R;\n",
    "}\n",
    "\n",
    "parameters {\n",
    "    real logmean_SI;\n",
    "    real logsd_SI;\n",
    "\n",
    "    vector<lower = 0, upper = 1>[N] s_raw;\n",
    "    vector<lower = 0, upper = 1>[N] e_raw;\n",
    "}\n",
    "\n",
    "transformed parameters {\n",
    "    real<lower = 0> param2 = sqrt(log((exp(2*(logsd_SI-logmean_SI))+1.0)));\n",
    "    real param1 = logmean_SI - param2^2/2.0;\n",
    "\n",
    "    vector<lower = min(S_L), upper = max(S_R)>[N] s;\n",
    "    vector<lower = min(E_L), upper = max(E_R)>[N] e;\n",
    "\n",
    "    s = S_L + (S_R - S_L) .* s_raw;\n",
    "    for (k in 1:N) \n",
    "        if (E_R[k] > s[k]) \n",
    "            e[k] = E_L[k] + (s[k] - E_L[k]) * e_raw[k];\n",
    "        else\n",
    "            e[k] = E_L[k] + (E_R[k] - E_L[k]) * e_raw[k];\n",
    "}\n",
    "\n",
    "model {\n",
    "    logmean_SI ~ std_normal();\n",
    "    logsd_SI ~ std_normal();\n",
    "\n",
    "    e_raw ~ normal(0.5, 1.0);\n",
    "    s_raw ~ normal(0.5, 1.0);\n",
    "\n",
    "    target += lognormal_lpdf(s - e | param1, param2);\n",
    "}\n",
    "\n",
    "generated quantities {\n",
    "    real<lower = 0> mean_SI = exp(param1 + square(param2) / 2);\n",
    "    real<lower = 0> sd_SI = sqrt((exp(square(param2)) - 1) * exp(2*param1 + square(param2)));\n",
    "\n",
    "    vector[N] log_likelihood;\n",
    "    for (k in 1:N) \n",
    "        log_likelihood[k] = lognormal_lpdf(s[k] - e[k] | param1, param2);\n",
    "}\" %>% cat(file=standirname %&% \"/fit.stan\", sep=\"\", fill=TRUE)\n",
    "\n",
    "standistribdir = \"../../../../../CmdStan-2.22.1\"\n",
    "stanscriptdir = \"../Dropbox/\" %&% substring(standirname,13)\n",
    "## bash file\n",
    "\"#!/bin/bash\n",
    "cwd=$(pwd)\n",
    "cd \"%&%standistribdir%&%\"\n",
    "make -j6 \"%&%stanscriptdir%&%\"/fit\n",
    "cd \"%&%stanscriptdir%&%\"\n",
    "mkdir -p diagnostics\n",
    "for i in {1..10}\n",
    "do\n",
    "    echo Running ${i}\n",
    "    SEEDNUMBER=$((1+$i))\n",
    "    ./fit \\\\\n",
    "        method=sample num_samples=10000 num_warmup=20000 save_warmup=0 \\\\\n",
    "            adapt delta=0.98 \\\\\n",
    "            algorithm=hmc \\\\\n",
    "                engine=nuts \\\\\n",
    "        random seed=${SEEDNUMBER} \\\\\n",
    "        id=$i \\\\\n",
    "        data file=Data.R \\\\\n",
    "        init=Init.R \\\\\n",
    "        output file=trace-$i.csv \\\\\n",
    "            diagnostic_file=diagnostics/diagnostics-$i.csv > diagnostics/output-$i.txt &\n",
    "done\n",
    "echo Finished sampling haha!\n",
    "\" %>% cat(file=standirname%&%\"/fit.sh\", sep=\"\", fill=TRUE)\n",
    "\n",
    "## running the bash script\n",
    "system(\"bash \"%&%standirname%&%\"/fit.sh\", intern = TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"maroon\">Gamma distribution</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>''</li><li>'--- Translating Stan model to C++ code ---'</li><li><span style=white-space:pre-wrap>'bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.stan'</span></li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.hpp'</span></li><li>''</li><li>'--- Compiling, linking C++ code ---'</li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.hpp'</span></li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit'</span></li><li>'Running 1'</li><li>'Running 2'</li><li>'Running 3'</li><li>'Running 4'</li><li>'Running 5'</li><li>'Running 6'</li><li>'Running 7'</li><li>'Running 8'</li><li>'Running 9'</li><li>'Running 10'</li><li>'Finished sampling haha!'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item ''\n",
       "\\item '--- Translating Stan model to C++ code ---'\n",
       "\\item 'bin/stanc  --o=../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-no\\_truncation/fit.hpp ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-no\\_truncation/fit.stan'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_4.1.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI   -c -MT ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-no\\_truncation/fit.o -MT ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-no\\_truncation/fit -include ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-no\\_truncation/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-no\\_truncation/fit.d ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-no\\_truncation/fit.hpp'\n",
       "\\item ''\n",
       "\\item '--- Compiling, linking C++ code ---'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_4.1.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI   -c  -x c++ -o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-no\\_truncation/fit.o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-no\\_truncation/fit.hpp'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_4.1.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan\\_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan\\_math/lib/tbb\"  ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-no\\_truncation/fit.o src/cmdstan/main.o         stan/lib/stan\\_math/lib/sundials\\_4.1.0/lib/libsundials\\_nvecserial.a stan/lib/stan\\_math/lib/sundials\\_4.1.0/lib/libsundials\\_cvodes.a stan/lib/stan\\_math/lib/sundials\\_4.1.0/lib/libsundials\\_idas.a stan/lib/stan\\_math/lib/sundials\\_4.1.0/lib/libsundials\\_kinsol.a stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib/libboost\\_serialization.so stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib/libboost\\_mpi.so stan/lib/stan\\_math/stan/math/prim/functor/mpi\\_cluster\\_inst.o stan/lib/stan\\_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-no\\_truncation/fit'\n",
       "\\item 'Running 1'\n",
       "\\item 'Running 2'\n",
       "\\item 'Running 3'\n",
       "\\item 'Running 4'\n",
       "\\item 'Running 5'\n",
       "\\item 'Running 6'\n",
       "\\item 'Running 7'\n",
       "\\item 'Running 8'\n",
       "\\item 'Running 9'\n",
       "\\item 'Running 10'\n",
       "\\item 'Finished sampling haha!'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. ''\n",
       "2. '--- Translating Stan model to C++ code ---'\n",
       "3. <span style=white-space:pre-wrap>'bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.stan'</span>\n",
       "4. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.hpp'</span>\n",
       "5. ''\n",
       "6. '--- Compiling, linking C++ code ---'\n",
       "7. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.hpp'</span>\n",
       "8. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit'</span>\n",
       "9. 'Running 1'\n",
       "10. 'Running 2'\n",
       "11. 'Running 3'\n",
       "12. 'Running 4'\n",
       "13. 'Running 5'\n",
       "14. 'Running 6'\n",
       "15. 'Running 7'\n",
       "16. 'Running 8'\n",
       "17. 'Running 9'\n",
       "18. 'Running 10'\n",
       "19. 'Finished sampling haha!'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        \n",
       " [2] \"--- Translating Stan model to C++ code ---\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              \n",
       " [3] \"bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.stan\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     \n",
       " [4] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.hpp\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         \n",
       " [5] \"\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        \n",
       " [6] \"--- Compiling, linking C++ code ---\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     \n",
       " [7] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.hpp\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        \n",
       " [8] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\\\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\\\" -Wl,-rpath,\\\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\\\" -Wl,-L,\\\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\\\" -Wl,-rpath,\\\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\\\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-no_truncation/fit\"\n",
       " [9] \"Running 1\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \n",
       "[10] \"Running 2\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \n",
       "[11] \"Running 3\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \n",
       "[12] \"Running 4\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \n",
       "[13] \"Running 5\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \n",
       "[14] \"Running 6\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \n",
       "[15] \"Running 7\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \n",
       "[16] \"Running 8\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \n",
       "[17] \"Running 9\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \n",
       "[18] \"Running 10\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              \n",
       "[19] \"Finished sampling haha!\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## main dir for Stan simulations\n",
    "standirname = stanmaindir%&%\"/gamma-no_truncation\"\n",
    "unlink(standirname, recursive=T)\n",
    "dir.create(standirname)\n",
    "\n",
    "# Dumping data\n",
    "N = nrow(df)\n",
    "E_L = df$EL\n",
    "E_R = df$ER\n",
    "S_L = df$SL\n",
    "S_R = df$SR\n",
    "stan_rdump(c('E_L', 'E_R', 'S_L', 'S_R', 'N'), file=standirname%&%\"/Data.R\") \n",
    "\n",
    "# Dumping initial conditions\n",
    "e_raw = rep(.2, N)\n",
    "s_raw = rep(.8, N)\n",
    "param1 = (mean(df$dist)/sd(df$dist))^2\n",
    "param2 = mean(df$dist)/(sd(df$dist)^2)\n",
    "stan_rdump(c('e_raw', 's_raw', 'param1', 'param2'), file=standirname%&%\"/Init.R\") \n",
    "\n",
    "# Stan program\n",
    "\"data {\n",
    "    int<lower = 0> N; // number of records\n",
    "    vector<lower = 0>[N] E_L;\n",
    "    vector<lower = 0>[N] E_R;\n",
    "    vector<lower = 0>[N] S_L;\n",
    "    vector<lower = 0>[N] S_R;\n",
    "}\n",
    "\n",
    "parameters {\n",
    "    real<lower=0> mean_SI;\n",
    "    real<lower=0> sd_SI;\n",
    "\n",
    "    vector<lower = 0, upper = 1>[N] e_raw;\n",
    "    vector<lower = 0, upper = 1>[N] s_raw;\n",
    "}\n",
    "\n",
    "transformed parameters {\n",
    "    real<lower = 0> param1 = square(mean_SI/sd_SI);\n",
    "    real<lower = 0> param2 = mean_SI/square(sd_SI);\n",
    "\n",
    "    vector<lower = min(S_L), upper = max(S_R)>[N] s;\n",
    "    vector<lower = min(E_L), upper = max(E_R)>[N] e;\n",
    "\n",
    "    s = S_L + (S_R - S_L) .* s_raw;\n",
    "    for (k in 1:N) \n",
    "        if (E_R[k] > s[k]) \n",
    "            e[k] = E_L[k] + (s[k] - E_L[k]) * e_raw[k];\n",
    "        else\n",
    "            e[k] = E_L[k] + (E_R[k] - E_L[k]) * e_raw[k];\n",
    "}\n",
    "\n",
    "model {\n",
    "    mean_SI ~ normal(5.0, 10.0);\n",
    "    sd_SI ~ cauchy(0, 5.0);\n",
    "\n",
    "    e_raw ~ normal(0.5, 1.0);\n",
    "    s_raw ~ normal(0.5, 1.0);\n",
    "\n",
    "    target += gamma_lpdf(s - e | param1, param2);\n",
    "}\n",
    "\n",
    "generated quantities {\n",
    "    vector[N] log_likelihood;\n",
    "    for (k in 1:N) \n",
    "        log_likelihood[k] = gamma_lpdf(s[k] - e[k] | param1, param2);\n",
    "}\" %>% cat(file=standirname %&% \"/fit.stan\", sep=\"\", fill=TRUE)\n",
    "\n",
    "standistribdir = \"../../../../../CmdStan-2.22.1\"\n",
    "stanscriptdir = \"../Dropbox/\" %&% substring(standirname,13)\n",
    "## bash file\n",
    "\"#!/bin/bash\n",
    "cwd=$(pwd)\n",
    "cd \"%&%standistribdir%&%\"\n",
    "make -j6 \"%&%stanscriptdir%&%\"/fit\n",
    "cd \"%&%stanscriptdir%&%\"\n",
    "mkdir -p diagnostics\n",
    "for i in {1..10}\n",
    "do\n",
    "    echo Running ${i}\n",
    "    SEEDNUMBER=$((1+$i))\n",
    "    ./fit \\\\\n",
    "        method=sample num_samples=10000 num_warmup=20000 save_warmup=0 \\\\\n",
    "            adapt delta=0.98 \\\\\n",
    "            algorithm=hmc \\\\\n",
    "                engine=nuts \\\\\n",
    "        random seed=${SEEDNUMBER} \\\\\n",
    "        id=$i \\\\\n",
    "        data file=Data.R \\\\\n",
    "        init=Init.R \\\\\n",
    "        output file=trace-$i.csv \\\\\n",
    "            refresh=1000 \\\\\n",
    "            diagnostic_file=diagnostics/diagnostics-$i.csv > diagnostics/output-$i.txt &\n",
    "done\n",
    "echo Finished sampling haha!\n",
    "\" %>% cat(file=standirname%&%\"/fit.sh\", sep=\"\", fill=TRUE)\n",
    "\n",
    "## running the bash script\n",
    "system(\"bash \"%&%standirname%&%\"/fit.sh\", intern = TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"maroon\">Weibull distribution</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>''</li><li>'--- Translating Stan model to C++ code ---'</li><li><span style=white-space:pre-wrap>'bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.stan'</span></li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.hpp'</span></li><li>''</li><li>'--- Compiling, linking C++ code ---'</li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.hpp'</span></li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit'</span></li><li>'Running 1'</li><li>'Running 2'</li><li>'Running 3'</li><li>'Running 4'</li><li>'Running 5'</li><li>'Running 6'</li><li>'Running 7'</li><li>'Running 8'</li><li>'Running 9'</li><li>'Running 10'</li><li>'Finished sampling haha!'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item ''\n",
       "\\item '--- Translating Stan model to C++ code ---'\n",
       "\\item 'bin/stanc  --o=../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-no\\_truncation/fit.hpp ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-no\\_truncation/fit.stan'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_4.1.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI   -c -MT ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-no\\_truncation/fit.o -MT ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-no\\_truncation/fit -include ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-no\\_truncation/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-no\\_truncation/fit.d ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-no\\_truncation/fit.hpp'\n",
       "\\item ''\n",
       "\\item '--- Compiling, linking C++ code ---'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_4.1.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI   -c  -x c++ -o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-no\\_truncation/fit.o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-no\\_truncation/fit.hpp'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_4.1.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan\\_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan\\_math/lib/tbb\"  ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-no\\_truncation/fit.o src/cmdstan/main.o         stan/lib/stan\\_math/lib/sundials\\_4.1.0/lib/libsundials\\_nvecserial.a stan/lib/stan\\_math/lib/sundials\\_4.1.0/lib/libsundials\\_cvodes.a stan/lib/stan\\_math/lib/sundials\\_4.1.0/lib/libsundials\\_idas.a stan/lib/stan\\_math/lib/sundials\\_4.1.0/lib/libsundials\\_kinsol.a stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib/libboost\\_serialization.so stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib/libboost\\_mpi.so stan/lib/stan\\_math/stan/math/prim/functor/mpi\\_cluster\\_inst.o stan/lib/stan\\_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-no\\_truncation/fit'\n",
       "\\item 'Running 1'\n",
       "\\item 'Running 2'\n",
       "\\item 'Running 3'\n",
       "\\item 'Running 4'\n",
       "\\item 'Running 5'\n",
       "\\item 'Running 6'\n",
       "\\item 'Running 7'\n",
       "\\item 'Running 8'\n",
       "\\item 'Running 9'\n",
       "\\item 'Running 10'\n",
       "\\item 'Finished sampling haha!'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. ''\n",
       "2. '--- Translating Stan model to C++ code ---'\n",
       "3. <span style=white-space:pre-wrap>'bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.stan'</span>\n",
       "4. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.hpp'</span>\n",
       "5. ''\n",
       "6. '--- Compiling, linking C++ code ---'\n",
       "7. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.hpp'</span>\n",
       "8. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit'</span>\n",
       "9. 'Running 1'\n",
       "10. 'Running 2'\n",
       "11. 'Running 3'\n",
       "12. 'Running 4'\n",
       "13. 'Running 5'\n",
       "14. 'Running 6'\n",
       "15. 'Running 7'\n",
       "16. 'Running 8'\n",
       "17. 'Running 9'\n",
       "18. 'Running 10'\n",
       "19. 'Finished sampling haha!'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \n",
       " [2] \"--- Translating Stan model to C++ code ---\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  \n",
       " [3] \"bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.stan\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     \n",
       " [4] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.hpp\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       " [5] \"\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \n",
       " [6] \"--- Compiling, linking C++ code ---\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         \n",
       " [7] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.hpp\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        \n",
       " [8] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\\\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\\\" -Wl,-rpath,\\\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\\\" -Wl,-L,\\\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\\\" -Wl,-rpath,\\\"/home/aakhmetz/CmdStan-2.22.1/stan/lib/stan_math/lib/tbb\\\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-no_truncation/fit\"\n",
       " [9] \"Running 1\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[10] \"Running 2\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[11] \"Running 3\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[12] \"Running 4\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[13] \"Running 5\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[14] \"Running 6\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[15] \"Running 7\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[16] \"Running 8\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[17] \"Running 9\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[18] \"Running 10\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  \n",
       "[19] \"Finished sampling haha!\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## main dir for Stan simulations\n",
    "standirname = stanmaindir%&%\"/weibull-no_truncation\"\n",
    "unlink(standirname, recursive=T)\n",
    "dir.create(standirname)\n",
    "\n",
    "# Dumping data\n",
    "N = nrow(df)\n",
    "E_L = df$EL\n",
    "E_R = df$ER\n",
    "S_L = df$SL\n",
    "S_R = df$SR\n",
    "stan_rdump(c('E_L', 'E_R', 'S_L', 'S_R', 'N'), file=standirname%&%\"/Data.R\") \n",
    "\n",
    "# Dumping initial conditions\n",
    "e_raw = rep(.2, N)\n",
    "s_raw = rep(.8, N)\n",
    "logmean_SI = log(mean(df$dist))\n",
    "param1 = 1.75\n",
    "stan_rdump(c('e_raw', 's_raw', 'logmean_SI', 'param1'), file=standirname%&%\"/Init.R\") \n",
    "\n",
    "# Stan program\n",
    "\"data {\n",
    "    int<lower = 0> N; // number of records\n",
    "    vector<lower = 0>[N] E_L;\n",
    "    vector<lower = 0>[N] E_R;\n",
    "    vector<lower = 0>[N] S_L;\n",
    "    vector<lower = 0>[N] S_R;\n",
    "}\n",
    "\n",
    "parameters {\n",
    "    real<lower = 0> mean_SI;\n",
    "    real<lower = 0> param1;\n",
    "\n",
    "    vector<lower = 0, upper = 1>[N] e_raw;\n",
    "    vector<lower = 0, upper = 1>[N] s_raw;\n",
    "}\n",
    "\n",
    "transformed parameters {\n",
    "    real<lower = 0> param2 = mean_SI/tgamma(1.0+1.0/param1);\n",
    "\n",
    "    vector<lower = min(S_L), upper = max(S_R)>[N] s;\n",
    "    vector<lower = min(E_L), upper = max(E_R)>[N] e;\n",
    "\n",
    "    s = S_L + (S_R - S_L) .* s_raw;\n",
    "    for (k in 1:N) \n",
    "        if (E_R[k] > s[k]) \n",
    "            e[k] = E_L[k] + (s[k] - E_L[k]) * e_raw[k];\n",
    "        else\n",
    "            e[k] = E_L[k] + (E_R[k] - E_L[k]) * e_raw[k];\n",
    "}\n",
    "\n",
    "model {\n",
    "    mean_SI ~ normal(5.0, 10.0);\n",
    "    param1 ~ exponential(0.0001);\n",
    "\n",
    "    e_raw ~ normal(0.5, 1.0);\n",
    "    s_raw ~ normal(0.5, 1.0);\n",
    "\n",
    "    target += weibull_lpdf(s - e | param1, param2);\n",
    "}\n",
    "\n",
    "generated quantities {\n",
    "    real sd_SI = param2*sqrt(tgamma(1.0+2.0/param1) - square(tgamma(1.0+1.0/param1)));\n",
    "\n",
    "    vector[N] log_likelihood;\n",
    "    for (k in 1:N) \n",
    "        log_likelihood[k] = weibull_lpdf(s[k] - e[k] | param1, param2);\n",
    "}\" %>% cat(file=standirname %&% \"/fit.stan\", sep=\"\", fill=TRUE)\n",
    "\n",
    "standistribdir = \"../../../../../CmdStan-2.22.1\"\n",
    "stanscriptdir = \"../Dropbox/\" %&% substring(standirname,13)\n",
    "## bash file\n",
    "\"#!/bin/bash\n",
    "cwd=$(pwd)\n",
    "cd \"%&%standistribdir%&%\"\n",
    "make -j6 \"%&%stanscriptdir%&%\"/fit\n",
    "cd \"%&%stanscriptdir%&%\"\n",
    "mkdir -p diagnostics\n",
    "for i in {1..10}\n",
    "do\n",
    "    echo Running ${i}\n",
    "    SEEDNUMBER=$((1+$i))\n",
    "    ./fit \\\\\n",
    "        method=sample num_samples=10000 num_warmup=10000 save_warmup=0 \\\\\n",
    "            adapt delta=0.98 \\\\\n",
    "            algorithm=hmc \\\\\n",
    "                engine=nuts \\\\\n",
    "        random seed=${SEEDNUMBER} \\\\\n",
    "        id=$i \\\\\n",
    "        data file=Data.R \\\\\n",
    "        init=Init.R \\\\\n",
    "        output file=trace-$i.csv \\\\\n",
    "            diagnostic_file=diagnostics/diagnostics-$i.csv > diagnostics/output-$i.txt &\n",
    "done\n",
    "echo Finished sampling haha!\n",
    "\" %>% cat(file=standirname%&%\"/fit.sh\", sep=\"\", fill=TRUE)\n",
    "\n",
    "## running the bash script\n",
    "system(\"bash \"%&%standirname%&%\"/fit.sh\", intern = TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# With truncation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Lognormal distribution</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>''</li><li>'--- Translating Stan model to C++ code ---'</li><li><span style=white-space:pre-wrap>'bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.stan'</span></li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.hpp'</span></li><li>''</li><li>'--- Compiling, linking C++ code ---'</li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.hpp'</span></li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit'</span></li><li>'Running 1'</li><li>'Running 2'</li><li>'Running 3'</li><li>'Running 4'</li><li>'Running 5'</li><li>'Running 6'</li><li>'Running 7'</li><li>'Running 8'</li><li>'Running 9'</li><li>'Running 10'</li><li>'Finished sampling haha!'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item ''\n",
       "\\item '--- Translating Stan model to C++ code ---'\n",
       "\\item 'bin/stanc  --o=../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-truncated/fit.hpp ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-truncated/fit.stan'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_5.2.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI   -c -MT ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-truncated/fit.o -MT ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-truncated/fit -include ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-truncated/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-truncated/fit.d ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-truncated/fit.hpp'\n",
       "\\item ''\n",
       "\\item '--- Compiling, linking C++ code ---'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_5.2.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI   -c  -x c++ -o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-truncated/fit.o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-truncated/fit.hpp'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_5.2.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan\\_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan\\_math/lib/tbb\"  ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-truncated/fit.o src/cmdstan/main.o         stan/lib/stan\\_math/lib/sundials\\_5.2.0/lib/libsundials\\_nvecserial.a stan/lib/stan\\_math/lib/sundials\\_5.2.0/lib/libsundials\\_cvodes.a stan/lib/stan\\_math/lib/sundials\\_5.2.0/lib/libsundials\\_idas.a stan/lib/stan\\_math/lib/sundials\\_5.2.0/lib/libsundials\\_kinsol.a stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib/libboost\\_serialization.so stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib/libboost\\_mpi.so stan/lib/stan\\_math/stan/math/prim/functor/mpi\\_cluster\\_inst.o stan/lib/stan\\_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/lognormal-truncated/fit'\n",
       "\\item 'Running 1'\n",
       "\\item 'Running 2'\n",
       "\\item 'Running 3'\n",
       "\\item 'Running 4'\n",
       "\\item 'Running 5'\n",
       "\\item 'Running 6'\n",
       "\\item 'Running 7'\n",
       "\\item 'Running 8'\n",
       "\\item 'Running 9'\n",
       "\\item 'Running 10'\n",
       "\\item 'Finished sampling haha!'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. ''\n",
       "2. '--- Translating Stan model to C++ code ---'\n",
       "3. <span style=white-space:pre-wrap>'bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.stan'</span>\n",
       "4. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.hpp'</span>\n",
       "5. ''\n",
       "6. '--- Compiling, linking C++ code ---'\n",
       "7. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.hpp'</span>\n",
       "8. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit'</span>\n",
       "9. 'Running 1'\n",
       "10. 'Running 2'\n",
       "11. 'Running 3'\n",
       "12. 'Running 4'\n",
       "13. 'Running 5'\n",
       "14. 'Running 6'\n",
       "15. 'Running 7'\n",
       "16. 'Running 8'\n",
       "17. 'Running 9'\n",
       "18. 'Running 10'\n",
       "19. 'Finished sampling haha!'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \n",
       " [2] \"--- Translating Stan model to C++ code ---\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  \n",
       " [3] \"bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.stan\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         \n",
       " [4] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.hpp\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \n",
       " [5] \"\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \n",
       " [6] \"--- Compiling, linking C++ code ---\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         \n",
       " [7] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.hpp\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \n",
       " [8] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\\\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\\\" -Wl,-rpath,\\\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\\\" -Wl,-L,\\\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\\\" -Wl,-rpath,\\\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\\\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/lognormal-truncated/fit\"\n",
       " [9] \"Running 1\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[10] \"Running 2\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[11] \"Running 3\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[12] \"Running 4\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[13] \"Running 5\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[14] \"Running 6\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[15] \"Running 7\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[16] \"Running 8\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[17] \"Running 9\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       "[18] \"Running 10\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  \n",
       "[19] \"Finished sampling haha!\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## main dir for Stan simulations\n",
    "standirname = stanmaindir%&%\"/lognormal-truncated\"\n",
    "unlink(standirname, recursive=T)\n",
    "dir.create(standirname)\n",
    "\n",
    "# Dumping data\n",
    "N = nrow(df)\n",
    "E_L = df$EL\n",
    "E_R = df$ER\n",
    "S_L = df$SL\n",
    "S_R = df$SR\n",
    "r = 0.14\n",
    "upper_bound = df$tstar[1]\n",
    "stan_rdump(c('E_L', 'E_R', 'S_L', 'S_R', 'N', 'r', 'upper_bound'), file=standirname%&%\"/Data.R\") \n",
    "\n",
    "# Dumping initial conditions\n",
    "e_raw = rep(.2, N)\n",
    "s_raw = rep(.8, N)\n",
    "logmean_SI = log(mean(df$dist))\n",
    "logsd_SI = log(sd(df$dist))\n",
    "stan_rdump(c('e_raw', 's_raw', 'logmean_SI', 'logsd_SI'), file=standirname%&%\"/Init.R\") \n",
    "\n",
    "# Stan program\n",
    "\"functions {\n",
    "    real[] fstar_ode(real t, real[] z, real[] theta, data real[] x_r, int[] x_i) {\n",
    "        int N = x_i[1]; // number of records\n",
    "\n",
    "        real e[N] = theta[1:N];\n",
    "        real param1 = theta[N+1];\n",
    "        real param2 = theta[N+2];\n",
    "\n",
    "        real upper_bound = x_r[1];\n",
    "        real r = x_r[2];\n",
    "\n",
    "        real dzdt[N];\n",
    "        real tstar[N];\n",
    "\n",
    "        for (k in 1:N) {\n",
    "            tstar[k] = upper_bound - e[k];\n",
    "            dzdt[k] = exp(lognormal_lcdf(tstar[k]*(1.0-t) | param1, param2)) * r * tstar[k] * exp(-r*tstar[k]*t) / (1.0 - exp(-r*tstar[k]*t));\n",
    "        }\n",
    "\n",
    "        return dzdt;\n",
    "    }\n",
    "}\n",
    "\n",
    "data {\n",
    "    int<lower = 0> N; // number of records\n",
    "    vector<lower = 0>[N] E_L;\n",
    "    vector<lower = 0>[N] E_R;\n",
    "    vector<lower = 0>[N] S_L;\n",
    "    vector<lower = 0>[N] S_R;\n",
    "    real<lower = 0> upper_bound;\n",
    "    real<lower = 0> r;\n",
    "}\n",
    "\n",
    "transformed data {\n",
    "    int X_i[1] = {N};\n",
    "\n",
    "    real X_r[2] = {upper_bound, r};\n",
    "}\n",
    "\n",
    "parameters {\n",
    "    real logmean_SI;\n",
    "    real logsd_SI;\n",
    "\n",
    "    vector<lower = 0, upper = 1>[N] e_raw;\n",
    "    vector<lower = 0, upper = 1>[N] s_raw;\n",
    "}\n",
    "\n",
    "transformed parameters {\n",
    "    real<lower = 0> param2 = sqrt(log((exp(2*(logsd_SI-logmean_SI))+1.0)));\n",
    "    real param1 = logmean_SI - square(param2)/2.0;\n",
    "\n",
    "    vector<lower = min(E_L), upper = max(E_R)>[N] e;\n",
    "    vector<lower = min(S_L), upper = max(S_R)>[N] s;\n",
    "\n",
    "    vector[N] Z; \n",
    "    \n",
    "    {\n",
    "        real theta[N+2];\n",
    "        real Z0[N];\n",
    "        \n",
    "        s = S_L + (S_R - S_L) .* s_raw;\n",
    "        for (k in 1:N) \n",
    "            if (E_R[k] > s[k]) \n",
    "                e[k] = E_L[k] + (s[k] - E_L[k]) * e_raw[k];\n",
    "            else\n",
    "                e[k] = E_L[k] + (E_R[k] - E_L[k]) * e_raw[k];\n",
    "\n",
    "        for (k in 1:N) {\n",
    "            Z0[k] = 0.0;\n",
    "            theta[k] = e[k];\n",
    "        }\n",
    "        theta[N+1] = param1;\n",
    "        theta[N+2] = param2;\n",
    "\n",
    "        Z = to_vector(to_array_1d(integrate_ode_rk45(fstar_ode, Z0, 0.001, {1.0}, theta, X_r, X_i, 1e-5, 1e-3, 5e2)));\n",
    "    }\n",
    "}\n",
    "\n",
    "model {\n",
    "    logmean_SI ~ std_normal();\n",
    "    logsd_SI ~ std_normal();\n",
    "\n",
    "    e_raw ~ normal(0.5, 1.0);\n",
    "    s_raw ~ normal(0.5, 1.0);\n",
    "\n",
    "    target += lognormal_lpdf(s - e | param1, param2) - log(Z);\n",
    "}\n",
    "\n",
    "generated quantities {\n",
    "    real<lower = 0> mean_SI = exp(param1 + square(param2)/2);\n",
    "    real<lower = 0> sd_SI = sqrt((exp(square(param2))-1)*exp(2*param1+square(param2)));\n",
    "\n",
    "    vector[N] log_likelihood;\n",
    "    for (k in 1:N)\n",
    "        log_likelihood[k] = lognormal_lpdf(s[k] - e[k] | param1, param2) - log(Z[k]);\n",
    "}\" %>% cat(file=standirname %&% \"/fit.stan\", sep=\"\", fill=TRUE)\n",
    "\n",
    "standistribdir = \"../../../../../CmdStan-2.22.1\"\n",
    "stanscriptdir = \"../Dropbox/\" %&% substring(standirname,13)\n",
    "## bash file\n",
    "\"#!/bin/bash\n",
    "cwd=$(pwd)\n",
    "cd \"%&%standistribdir%&%\"\n",
    "make -j6 \"%&%stanscriptdir%&%\"/fit\n",
    "cd \"%&%stanscriptdir%&%\"\n",
    "mkdir -p diagnostics\n",
    "for i in {1..10}\n",
    "do\n",
    "    echo Running ${i}\n",
    "    SEEDNUMBER=$((1+$i))\n",
    "    ./fit \\\\\n",
    "        method=sample num_samples=10000 num_warmup=10000 save_warmup=0 \\\\\n",
    "            adapt delta=0.98 \\\\\n",
    "            algorithm=hmc \\\\\n",
    "                engine=nuts \\\\\n",
    "        random seed=${SEEDNUMBER} \\\\\n",
    "        id=$i \\\\\n",
    "        data file=Data.R \\\\\n",
    "        init=Init.R \\\\\n",
    "        output file=trace-$i.csv \\\\\n",
    "            diagnostic_file=diagnostics/diagnostics-$i.csv > diagnostics/output-$i.txt &\n",
    "done\n",
    "echo Finished sampling haha!\n",
    "\" %>% cat(file=standirname%&%\"/fit.sh\", sep=\"\", fill=TRUE)\n",
    "\n",
    "## running the bash script\n",
    "system(\"bash \"%&%standirname%&%\"/fit.sh\", intern = TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Gamma distribution</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>''</li><li>'--- Translating Stan model to C++ code ---'</li><li><span style=white-space:pre-wrap>'bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.stan'</span></li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.hpp'</span></li><li>''</li><li>'--- Compiling, linking C++ code ---'</li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.hpp'</span></li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit'</span></li><li>'Running 1'</li><li>'Running 2'</li><li>'Running 3'</li><li>'Running 4'</li><li>'Running 5'</li><li>'Running 6'</li><li>'Running 7'</li><li>'Running 8'</li><li>'Running 9'</li><li>'Running 10'</li><li>'Finished sampling haha!'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item ''\n",
       "\\item '--- Translating Stan model to C++ code ---'\n",
       "\\item 'bin/stanc  --o=../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-truncated/fit.hpp ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-truncated/fit.stan'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_5.2.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI   -c -MT ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-truncated/fit.o -MT ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-truncated/fit -include ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-truncated/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-truncated/fit.d ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-truncated/fit.hpp'\n",
       "\\item ''\n",
       "\\item '--- Compiling, linking C++ code ---'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_5.2.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI   -c  -x c++ -o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-truncated/fit.o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-truncated/fit.hpp'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_5.2.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan\\_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan\\_math/lib/tbb\"  ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-truncated/fit.o src/cmdstan/main.o         stan/lib/stan\\_math/lib/sundials\\_5.2.0/lib/libsundials\\_nvecserial.a stan/lib/stan\\_math/lib/sundials\\_5.2.0/lib/libsundials\\_cvodes.a stan/lib/stan\\_math/lib/sundials\\_5.2.0/lib/libsundials\\_idas.a stan/lib/stan\\_math/lib/sundials\\_5.2.0/lib/libsundials\\_kinsol.a stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib/libboost\\_serialization.so stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib/libboost\\_mpi.so stan/lib/stan\\_math/stan/math/prim/functor/mpi\\_cluster\\_inst.o stan/lib/stan\\_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/gamma-truncated/fit'\n",
       "\\item 'Running 1'\n",
       "\\item 'Running 2'\n",
       "\\item 'Running 3'\n",
       "\\item 'Running 4'\n",
       "\\item 'Running 5'\n",
       "\\item 'Running 6'\n",
       "\\item 'Running 7'\n",
       "\\item 'Running 8'\n",
       "\\item 'Running 9'\n",
       "\\item 'Running 10'\n",
       "\\item 'Finished sampling haha!'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. ''\n",
       "2. '--- Translating Stan model to C++ code ---'\n",
       "3. <span style=white-space:pre-wrap>'bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.stan'</span>\n",
       "4. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.hpp'</span>\n",
       "5. ''\n",
       "6. '--- Compiling, linking C++ code ---'\n",
       "7. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.hpp'</span>\n",
       "8. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit'</span>\n",
       "9. 'Running 1'\n",
       "10. 'Running 2'\n",
       "11. 'Running 3'\n",
       "12. 'Running 4'\n",
       "13. 'Running 5'\n",
       "14. 'Running 6'\n",
       "15. 'Running 7'\n",
       "16. 'Running 8'\n",
       "17. 'Running 9'\n",
       "18. 'Running 10'\n",
       "19. 'Finished sampling haha!'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    \n",
       " [2] \"--- Translating Stan model to C++ code ---\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          \n",
       " [3] \"bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.stan\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         \n",
       " [4] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.hpp\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         \n",
       " [5] \"\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    \n",
       " [6] \"--- Compiling, linking C++ code ---\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 \n",
       " [7] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.hpp\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \n",
       " [8] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\\\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\\\" -Wl,-rpath,\\\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\\\" -Wl,-L,\\\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\\\" -Wl,-rpath,\\\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\\\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/gamma-truncated/fit\"\n",
       " [9] \"Running 1\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           \n",
       "[10] \"Running 2\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           \n",
       "[11] \"Running 3\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           \n",
       "[12] \"Running 4\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           \n",
       "[13] \"Running 5\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           \n",
       "[14] \"Running 6\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           \n",
       "[15] \"Running 7\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           \n",
       "[16] \"Running 8\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           \n",
       "[17] \"Running 9\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           \n",
       "[18] \"Running 10\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          \n",
       "[19] \"Finished sampling haha!\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## main dir for Stan simulations\n",
    "standirname = stanmaindir%&%\"/gamma-truncated\"\n",
    "unlink(standirname, recursive=T)\n",
    "dir.create(standirname)\n",
    "\n",
    "# Dumping data\n",
    "N = nrow(df)\n",
    "E_L = df$EL\n",
    "E_R = df$ER\n",
    "S_L = df$SL\n",
    "S_R = df$SR\n",
    "r = 0.14\n",
    "upper_bound = df$tstar[1]\n",
    "stan_rdump(c('E_L', 'E_R', 'S_L', 'S_R', 'N', 'r', 'upper_bound'), file=standirname%&%\"/Data.R\") \n",
    "\n",
    "# Dumping initial conditions\n",
    "e_raw = rep(.4, N)\n",
    "s_raw = rep(.6, N)\n",
    "mean_SI = mean(df$dist)\n",
    "sd_SI = sd(df$dist)\n",
    "stan_rdump(c('e_raw', 's_raw', 'mean_SI', 'sd_SI'), file=standirname%&%\"/Init.R\") \n",
    "\n",
    "# Stan program\n",
    "\"functions {\n",
    "    real[] fstar_ode(real t, real[] z, real[] theta, data real[] x_r, int[] x_i) {\n",
    "        int N = x_i[1]; // number of records\n",
    "\n",
    "        real e[N] = theta[1:N];\n",
    "        real param1 = theta[N+1];\n",
    "        real param2 = theta[N+2];\n",
    "\n",
    "        real upper_bound = x_r[1];\n",
    "        real r = x_r[2];\n",
    "\n",
    "        real dzdt[N];\n",
    "        real tstar[N];\n",
    "\n",
    "        for (k in 1:N) {\n",
    "            tstar[k] = upper_bound - e[k];\n",
    "            dzdt[k] = exp(gamma_lcdf(tstar[k]*(1.0-t) | param1, param2)) * r * tstar[k] * exp(-r*tstar[k]*t) / (1.0 - exp(-r*tstar[k]*t));\n",
    "        }\n",
    "\n",
    "        return dzdt;\n",
    "    }\n",
    "}\n",
    "\n",
    "data {\n",
    "    int<lower = 0> N; // number of records\n",
    "    vector<lower = 0>[N] E_L;\n",
    "    vector<lower = 0>[N] E_R;\n",
    "    vector<lower = 0>[N] S_L;\n",
    "    vector<lower = 0>[N] S_R;\n",
    "    real<lower = 0> r;\n",
    "    real<lower = 0> upper_bound;\n",
    "}\n",
    "\n",
    "transformed data {\n",
    "    int X_i[1] = {N};\n",
    "\n",
    "    real X_r[2] = {upper_bound, r};\n",
    "}\n",
    "\n",
    "parameters {\n",
    "    real<lower = 0> mean_SI;\n",
    "    real<lower = 0> sd_SI;\n",
    "\n",
    "    vector<lower = 0, upper = 1>[N] s_raw;\n",
    "    vector<lower = 0, upper = 1>[N] e_raw;\n",
    "}\n",
    "\n",
    "transformed parameters {\n",
    "    real<lower = 0> param1 = square(mean_SI/sd_SI);\n",
    "    real<lower = 0> param2 = mean_SI/square(sd_SI);\n",
    "\n",
    "    vector<lower = min(S_L), upper = max(S_R)>[N] s;\n",
    "    vector<lower = min(E_L), upper = max(E_R)>[N] e;\n",
    "\n",
    "    vector[N] Z; \n",
    "    \n",
    "    {\n",
    "        real theta[N+2];\n",
    "        real Z0[N];\n",
    "        \n",
    "        s = S_L + (S_R - S_L) .* s_raw;\n",
    "        for (k in 1:N) \n",
    "            if (E_R[k] > s[k]) \n",
    "                e[k] = E_L[k] + (s[k] - E_L[k]) * e_raw[k];\n",
    "            else\n",
    "                e[k] = E_L[k] + (E_R[k] - E_L[k]) * e_raw[k];\n",
    "\n",
    "        for (k in 1:N) {\n",
    "            Z0[k] = 0.0;\n",
    "            theta[k] = e[k];\n",
    "        }\n",
    "        theta[N+1] = param1;\n",
    "        theta[N+2] = param2;\n",
    "\n",
    "        Z = to_vector(to_array_1d(integrate_ode_rk45(fstar_ode, Z0, 0.001, {1.0}, theta, X_r, X_i)));\n",
    "    }\n",
    "}\n",
    "\n",
    "model {\n",
    "    mean_SI ~ normal(5.0, 10.0);\n",
    "    sd_SI ~ cauchy(0, 5.0);\n",
    "\n",
    "    e_raw ~ normal(0.5, 1.0);\n",
    "    s_raw ~ normal(0.5, 1.0);\n",
    "\n",
    "    target += gamma_lpdf(s - e | param1, param2) - log(Z);\n",
    "}\n",
    "\n",
    "generated quantities {\n",
    "    vector[N] log_likelihood;\n",
    "    for (k in 1:N) \n",
    "        log_likelihood[k] = gamma_lpdf(s[k] - e[k] | param1, param2) - log(Z[k]);\n",
    "}\" %>% cat(file=standirname %&% \"/fit.stan\", sep=\"\", fill=TRUE)\n",
    "\n",
    "standistribdir = \"../../../../../CmdStan\"\n",
    "stanscriptdir = \"../Dropbox/\" %&% substring(standirname,13)\n",
    "## bash file\n",
    "\"#!/bin/bash\n",
    "cwd=$(pwd)\n",
    "cd \"%&%standistribdir%&%\"\n",
    "make -j6 \"%&%stanscriptdir%&%\"/fit\n",
    "cd \"%&%stanscriptdir%&%\"\n",
    "mkdir -p diagnostics\n",
    "for i in {1..10}\n",
    "do\n",
    "    echo Running ${i}\n",
    "    SEEDNUMBER=$((1+$i))\n",
    "    ./fit \\\\\n",
    "        method=sample num_samples=10000 num_warmup=10000 save_warmup=0 \\\\\n",
    "            adapt delta=0.98 \\\\\n",
    "            algorithm=hmc \\\\\n",
    "                engine=nuts \\\\\n",
    "        random seed=${SEEDNUMBER} \\\\\n",
    "        id=$i \\\\\n",
    "        data file=Data.R \\\\\n",
    "        init=Init.R \\\\\n",
    "        output file=trace-$i.csv \\\\\n",
    "            diagnostic_file=diagnostics/diagnostics-$i.csv > diagnostics/output-$i.txt &\n",
    "done\n",
    "echo Finished sampling haha!\n",
    "\" %>% cat(file=standirname%&%\"/fit.sh\", sep=\"\", fill=TRUE)\n",
    "\n",
    "## running the bash script\n",
    "system(\"bash \"%&%standirname%&%\"/fit.sh\", intern = TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Weibull distribution</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>''</li><li>'--- Translating Stan model to C++ code ---'</li><li><span style=white-space:pre-wrap>'bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.stan'</span></li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.hpp'</span></li><li>''</li><li>'--- Compiling, linking C++ code ---'</li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.hpp'</span></li><li><span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit'</span></li><li>'Running 1'</li><li>'Running 2'</li><li>'Running 3'</li><li>'Running 4'</li><li>'Running 5'</li><li>'Running 6'</li><li>'Running 7'</li><li>'Running 8'</li><li>'Running 9'</li><li>'Running 10'</li><li>'Finished sampling haha!'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item ''\n",
       "\\item '--- Translating Stan model to C++ code ---'\n",
       "\\item 'bin/stanc  --o=../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-truncated-2.23.0/fit.hpp ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-truncated-2.23.0/fit.stan'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_5.2.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI   -c -MT ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-truncated-2.23.0/fit.o -MT ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-truncated-2.23.0/fit -include ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-truncated-2.23.0/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-truncated-2.23.0/fit.d ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-truncated-2.23.0/fit.hpp'\n",
       "\\item ''\n",
       "\\item '--- Compiling, linking C++ code ---'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_5.2.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI   -c  -x c++ -o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-truncated-2.23.0/fit.o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-truncated-2.23.0/fit.hpp'\n",
       "\\item 'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D\\_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan\\_math/lib/tbb\\_2019\\_U8/include -O3 -I src -I stan/src -I lib/rapidjson\\_1.1.0/ -I stan/lib/stan\\_math/ -I stan/lib/stan\\_math/lib/eigen\\_3.3.3 -I stan/lib/stan\\_math/lib/boost\\_1.72.0 -I stan/lib/stan\\_math/lib/sundials\\_5.2.0/include -DNDEBUG -D\\_FORTIFY\\_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST\\_DISABLE\\_ASSERTS   -DSTAN\\_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan\\_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan\\_math/lib/tbb\"  ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-truncated-2.23.0/fit.o src/cmdstan/main.o         stan/lib/stan\\_math/lib/sundials\\_5.2.0/lib/libsundials\\_nvecserial.a stan/lib/stan\\_math/lib/sundials\\_5.2.0/lib/libsundials\\_cvodes.a stan/lib/stan\\_math/lib/sundials\\_5.2.0/lib/libsundials\\_idas.a stan/lib/stan\\_math/lib/sundials\\_5.2.0/lib/libsundials\\_kinsol.a stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib/libboost\\_serialization.so stan/lib/stan\\_math/lib/boost\\_1.72.0/stage/lib/libboost\\_mpi.so stan/lib/stan\\_math/stan/math/prim/functor/mpi\\_cluster\\_inst.o stan/lib/stan\\_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido\\_Backup/Wuhan\\_Serial\\_interval\\_2020/certain/weibull-truncated-2.23.0/fit'\n",
       "\\item 'Running 1'\n",
       "\\item 'Running 2'\n",
       "\\item 'Running 3'\n",
       "\\item 'Running 4'\n",
       "\\item 'Running 5'\n",
       "\\item 'Running 6'\n",
       "\\item 'Running 7'\n",
       "\\item 'Running 8'\n",
       "\\item 'Running 9'\n",
       "\\item 'Running 10'\n",
       "\\item 'Finished sampling haha!'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. ''\n",
       "2. '--- Translating Stan model to C++ code ---'\n",
       "3. <span style=white-space:pre-wrap>'bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.stan'</span>\n",
       "4. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.hpp'</span>\n",
       "5. ''\n",
       "6. '--- Compiling, linking C++ code ---'\n",
       "7. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.hpp'</span>\n",
       "8. <span style=white-space:pre-wrap>'mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\" -Wl,-L,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\" -Wl,-rpath,\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit'</span>\n",
       "9. 'Running 1'\n",
       "10. 'Running 2'\n",
       "11. 'Running 3'\n",
       "12. 'Running 4'\n",
       "13. 'Running 5'\n",
       "14. 'Running 6'\n",
       "15. 'Running 7'\n",
       "16. 'Running 8'\n",
       "17. 'Running 9'\n",
       "18. 'Running 10'\n",
       "19. 'Finished sampling haha!'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      \n",
       " [2] \"--- Translating Stan model to C++ code ---\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \n",
       " [3] \"bin/stanc  --o=../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.hpp ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.stan\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         \n",
       " [4] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.o -MT ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit -include ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.hpp -include src/cmdstan/main.cpp -MM -E -MG -MP -MF ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.d ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.hpp\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              \n",
       " [5] \"\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      \n",
       " [6] \"--- Compiling, linking C++ code ---\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \n",
       " [7] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI   -c  -x c++ -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.hpp\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \n",
       " [8] \"mpicxx -fvisibility-inlines-hidden -std=c++17 -fmessage-length=0 -march=nocona -mtune=haswell -ftree-vectorize -fPIC -fstack-protector-strong -fno-plt -O2 -ffunction-sections -pipe -isystem /home/aakhmetz/anaconda3/include -std=c++1y -D_REENTRANT -Wno-sign-compare    -Wno-delete-non-virtual-dtor  -I stan/lib/stan_math/lib/tbb_2019_U8/include -O3 -I src -I stan/src -I lib/rapidjson_1.1.0/ -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.72.0 -I stan/lib/stan_math/lib/sundials_5.2.0/include -DNDEBUG -D_FORTIFY_SOURCE=2 -O2 -isystem /home/aakhmetz/anaconda3/include    -DBOOST_DISABLE_ASSERTS   -DSTAN_MPI  -Wl,-O2 -Wl,--sort-common -Wl,--as-needed -Wl,-z,relro -Wl,-z,now -Wl,--disable-new-dtags -Wl,--gc-sections -Wl,-rpath,/home/aakhmetz/anaconda3/lib -Wl,-rpath-link,/home/aakhmetz/anaconda3/lib -L/home/aakhmetz/anaconda3/lib       -Wl,-L,\\\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\\\" -Wl,-rpath,\\\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/boost_1.72.0/stage/lib\\\" -Wl,-L,\\\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\\\" -Wl,-rpath,\\\"/home/aakhmetz/CmdStan/stan/lib/stan_math/lib/tbb\\\"  ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit.o src/cmdstan/main.o         stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_idas.a stan/lib/stan_math/lib/sundials_5.2.0/lib/libsundials_kinsol.a stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_serialization.so stan/lib/stan_math/lib/boost_1.72.0/stage/lib/libboost_mpi.so stan/lib/stan_math/stan/math/prim/functor/mpi_cluster_inst.o stan/lib/stan_math/lib/tbb/libtbb.so.2 -o ../Dropbox/Hokkaido_Backup/Wuhan_Serial_interval_2020/certain/weibull-truncated-2.23.0/fit\"\n",
       " [9] \"Running 1\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \n",
       "[10] \"Running 2\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \n",
       "[11] \"Running 3\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \n",
       "[12] \"Running 4\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \n",
       "[13] \"Running 5\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \n",
       "[14] \"Running 6\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \n",
       "[15] \"Running 7\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \n",
       "[16] \"Running 8\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \n",
       "[17] \"Running 9\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \n",
       "[18] \"Running 10\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \n",
       "[19] \"Finished sampling haha!\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## main dir for Stan simulations\n",
    "standirname = stanmaindir%&%\"/weibull-truncated-2.23.0\"\n",
    "unlink(standirname, recursive=T)\n",
    "dir.create(standirname)\n",
    "\n",
    "# Dumping data\n",
    "N = nrow(df)\n",
    "E_L = df$EL\n",
    "E_R = df$ER\n",
    "S_L = df$SL\n",
    "S_R = df$SR\n",
    "r = 0.14\n",
    "upper_bound = df$tstar[1]\n",
    "stan_rdump(c('E_L', 'E_R', 'S_L', 'S_R', 'N', 'r', 'upper_bound'), file=standirname%&%\"/Data.R\") \n",
    "\n",
    "# Dumping initial conditions\n",
    "e_raw = rep(.2, N)\n",
    "s_raw = rep(.8, N)\n",
    "logmean_SI = log(mean(df$dist))\n",
    "param1 = 1.75\n",
    "stan_rdump(c('e_raw', 's_raw', 'logmean_SI', 'param1'), file=standirname%&%\"/Init.R\") \n",
    "\n",
    "# Stan program\n",
    "\"functions {\n",
    "    real[] fstar_ode(real t, real[] z, real[] theta, data real[] x_r, int[] x_i) {\n",
    "        int N = x_i[1]; // number of records\n",
    "\n",
    "        real e[N] = theta[1:N];\n",
    "        real param1 = theta[N+1];\n",
    "        real param2 = theta[N+2];\n",
    "\n",
    "        real upper_bound = x_r[1];\n",
    "        real r = x_r[2];\n",
    "\n",
    "        real dzdt[N];\n",
    "        real tstar[N];\n",
    "\n",
    "        for (k in 1:N) {\n",
    "            tstar[k] = upper_bound - e[k];\n",
    "            dzdt[k] = - expm1(-((1.0-t)*tstar[k]/param2)^param1) * r * tstar[k] * exp(-r*tstar[k]*t) / (1.0 - exp(-r*tstar[k]*t));\n",
    "        }\n",
    "\n",
    "        return dzdt;\n",
    "    }\n",
    "}\n",
    "\n",
    "data {\n",
    "    int<lower = 0> N; // number of records\n",
    "    vector<lower = 0>[N] E_L;\n",
    "    vector<lower = 0>[N] E_R;\n",
    "    vector<lower = 0>[N] S_L;\n",
    "    vector<lower = 0>[N] S_R;\n",
    "    real<lower = 0> r;\n",
    "    real<lower = 0> upper_bound;\n",
    "}\n",
    "\n",
    "transformed data {\n",
    "    int X_i[1] = {N};\n",
    "\n",
    "    real X_r[2] = {upper_bound, r};\n",
    "}\n",
    "\n",
    "parameters {\n",
    "    real<lower = 0> mean_SI;\n",
    "    real<lower = 0> param1;\n",
    "\n",
    "    vector<lower = 0, upper = 1>[N] e_raw;\n",
    "    vector<lower = 0, upper = 1>[N] s_raw;\n",
    "}\n",
    "\n",
    "transformed parameters {\n",
    "    real<lower = 0> param2 = mean_SI/tgamma(1.0+1.0/param1);\n",
    "\n",
    "    vector<lower = min(S_L), upper = max(S_R)>[N] s;\n",
    "    vector<lower = min(E_L), upper = max(E_R)>[N] e;\n",
    "\n",
    "    real Z[N]; \n",
    "    \n",
    "    {\n",
    "        vector[N] s_;\n",
    "        real theta[N+2];\n",
    "        real Z0[N];\n",
    "        \n",
    "        s = S_L + (S_R - S_L) .* s_raw;\n",
    "        for (k in 1:N) \n",
    "            if (E_R[k] > s[k]) \n",
    "                e[k] = E_L[k] + (s[k] - E_L[k]) * e_raw[k];\n",
    "            else\n",
    "                e[k] = E_L[k] + (E_R[k] - E_L[k]) * e_raw[k];\n",
    "\n",
    "        for (k in 1:N) {\n",
    "            Z0[k] = 0.0;\n",
    "            theta[k] = e[k];\n",
    "        }\n",
    "        theta[N+1] = param1;\n",
    "        theta[N+2] = param2;\n",
    "\n",
    "        Z = to_array_1d(integrate_ode_rk45(fstar_ode, Z0, 0.01, {1.0}, theta, X_r, X_i, 1e-5, 1e-3, 5e2));\n",
    "    }\n",
    "}\n",
    "\n",
    "model {\n",
    "    mean_SI ~ normal(5.0, 10.0);\n",
    "    param1 ~ exponential(0.0001);\n",
    "\n",
    "    e_raw ~ normal(0.5, 1.0);\n",
    "    s_raw ~ normal(0.5, 1.0);\n",
    "\n",
    "    for (k in 1:N) \n",
    "        target += weibull_lpdf(s[k] - e[k] | param1, param2) - log(Z[k]);\n",
    "}\n",
    "\n",
    "generated quantities {\n",
    "    real sd_SI = param2*sqrt(tgamma(1.0+2.0/param1)-(tgamma(1.0+1.0/param1))^2);\n",
    "\n",
    "    vector[N] log_likelihood;\n",
    "    for (k in 1:N) \n",
    "        log_likelihood[k] = weibull_lpdf(s[k] - e[k] | param1, param2) - log(Z[k]);\n",
    "}\" %>% cat(file=standirname %&% \"/fit.stan\", sep=\"\", fill=TRUE)\n",
    "\n",
    "standistribdir = \"../../../../../CmdStan\" #-2.22.1\n",
    "stanscriptdir = \"../Dropbox/\" %&% substring(standirname,13)\n",
    "## bash file\n",
    "\"#!/bin/bash\n",
    "cwd=$(pwd)\n",
    "cd \"%&%standistribdir%&%\"\n",
    "make -j6 \"%&%stanscriptdir%&%\"/fit\n",
    "cd \"%&%stanscriptdir%&%\"\n",
    "mkdir -p diagnostics\n",
    "for i in {1..10}\n",
    "do\n",
    "    echo Running ${i}\n",
    "    SEEDNUMBER=$((1+$i))\n",
    "    ./fit \\\\\n",
    "        method=sample num_samples=10000 num_warmup=10000 save_warmup=0 \\\\\n",
    "            adapt delta=0.98 \\\\\n",
    "            algorithm=hmc \\\\\n",
    "                engine=nuts \\\\\n",
    "        random seed=${SEEDNUMBER} \\\\\n",
    "        id=$i \\\\\n",
    "        data file=Data.R \\\\\n",
    "        init=Init.R \\\\\n",
    "        output file=trace-$i.csv \\\\\n",
    "            diagnostic_file=diagnostics/diagnostics-$i.csv > diagnostics/output-$i.txt &\n",
    "done\n",
    "echo Finished sampling haha!\n",
    "\" %>% cat(file=standirname%&%\"/fit.sh\", sep=\"\", fill=TRUE)\n",
    "\n",
    "## running the bash script\n",
    "system(\"bash \"%&%standirname%&%\"/fit.sh\", intern = TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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