test_pyprob.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PyProb Example\n",
    "This is a version of the text message example from From Chapter 1 of “Bayesian Methods for Hackers” by Cameron Davidson-Pilon rendered with pyprob\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Empirical distributions on disk may perform slow because GNU DBM is not available. Please install and configure gdbm library for Python for better speed.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pyprob\n",
    "from pyprob import Model\n",
    "from pyprob.distributions import Normal, Uniform, Exponential\n",
    "import torch\n",
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "fig = plt.figure();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import csv\n",
    "dat = []\n",
    "with open('txtdata.csv', newline='') as File:  \n",
    "    reader = csv.reader(File)\n",
    "    for row in reader:\n",
    "        dat.append(row[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[13. 24.  8. 24.  7. 35. 14. 11. 15. 11. 22. 22. 11. 57. 11. 19. 29.  6.\n",
      " 19. 12. 22. 12. 18. 72. 32.  9.  7. 13. 19. 23. 27. 20.  6. 17. 13. 10.\n",
      " 14.  6. 16. 15.  7.  2. 15. 15. 19. 70. 49.  7. 53. 22. 21. 31. 19. 11.\n",
      " 18. 20. 12. 35. 17. 23. 17.  4.  2. 31. 30. 13. 27.  0. 39. 37.  5. 14.\n",
      " 13. 22.]\n",
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73]\n",
      "19.743243243243242\n"
     ]
    }
   ],
   "source": [
    "ys = np.zeros(74)\n",
    "xs = []\n",
    "for i in range(74):\n",
    "    ys[i] = float(dat[i+1])\n",
    "    xs.append(i)\n",
    "print(ys)\n",
    "print(xs)\n",
    "ymean = ys.mean()\n",
    "print(ymean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "class my_model(Model):\n",
    "    def __init__(self, ymean, xmax, xs):\n",
    "        super().__init__(name='my_model') # give the model a name\n",
    "        self.prior_mean = ymean\n",
    "        self.xmax = xmax\n",
    "        self.prior_std = 1\n",
    "        self.likelihood_std = 1\n",
    "        self.xs = xs\n",
    "\n",
    "    def forward(self): # Needed to specifcy how the generative model is run forward\n",
    "        mu1 = pyprob.sample(Exponential(1.0/self.prior_mean ))# NOTE: sample -> denotes latent variables\n",
    "        mu2 = pyprob.sample(Exponential(1.0/self.prior_mean)) # NOTE: sample -> denotes latent variables\n",
    "        tau = pyprob.sample(Uniform(0,self.xmax))\n",
    "        \n",
    "        for i, x in enumerate(self.xs):\n",
    "            if tau.numpy() > x:\n",
    "                mu = mu1\n",
    "            else:\n",
    "                mu = mu2\n",
    "            likelihood = Normal(mu, self.likelihood_std)\n",
    "            pyprob.observe(likelihood, name='obs'+str(i))\n",
    "\n",
    "        # return the latent quantity of interest\n",
    "        #return mu1, mu2, tau\n",
    "        return mu1, mu2 , tau\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = my_model(ymean, len(xs), xs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "observdic = {}\n",
    "for i in range(74):\n",
    "    observdic[\"obs\"+str(i)] = ys[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time spent  | Time remain.| Progress             | Trace       | Accepted|Smp reuse| Traces/sec\n",
      "0d:00:01:57 | 0d:00:00:00 | #################### | 10000/10000 |   1.88% |  66.67% | 84.84       \n"
     ]
    }
   ],
   "source": [
    "posterior = model.posterior_results(\n",
    "                    num_traces=10000, # the number of samples estimating the posterior\n",
    "                    inference_engine=pyprob.InferenceEngine.RANDOM_WALK_METROPOLIS_HASTINGS, \n",
    "                    observe= observdic )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(tensor(17.8024), tensor(23.0156), tensor(44.1014))\n"
     ]
    }
   ],
   "source": [
    "print(posterior.sample())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean for lambda1 = tensor(17.6366)\n",
      "mean for lambda2 = tensor(22.6672)\n",
      "mean for tau = tensor(43.0090)\n"
     ]
    }
   ],
   "source": [
    "posterior_first = posterior.map(lambda v: v[0]) # extract var_0\n",
    "print(\"mean for lambda1 =\",posterior_first.mean)\n",
    "posterior_second = posterior.map(lambda v: v[1]) # extract var_1\n",
    "print(\"mean for lambda2 =\",posterior_second.mean)\n",
    "posterior_third = posterior.map(lambda v: v[2]) # extract var_2\n",
    "print(\"mean for tau =\",posterior_third.mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "posterior_first.plot_histogram(show=True, bins=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "posterior_second.plot_histogram(show=True, bins=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JUmcGMkmSpM4MZJIkSZ0ZyCRJkjpb0rsCmq5lR5yxXtnVxzypQ00kSdJCHCGTJEnqzEAmSZLUmYFMkiSpM88hE+C5ZpKk6fO9ZmGOkEmSJHXmCNkMGvcJRZIk9TPVQJbkQOBtwHbAu6rqmHm33xZ4H/BQ4DvAM6rq6mnWaRILBRaHVSVJ0jRM7ZBlku2A44EnAHsAhyTZY95iLwCuq6r7AccBx06rPpIkSYvVNM8h2wdYU1VXVdWNwCnAwfOWORg4qU2fDjwuSaZYJ0mSpEVnmocsdwGuGZlfC/zGQstU1U1JvgfcHfj2FOulRcZv3UiSZt00A9m4ka7ajGVIcihwaJv9QZIrb2HdNsXOtICYGTugmmNvbnuH++6tW9sXAds+m2z77Ora/p6v91vpfe7ekyw0zUC2FthtZH5X4NoFllmbZAlwF+C/5m+oqk4ATphSPTcoyeqqWtHjvnuz7bZ91th22z6LZrn9i6nt0zyH7HxgeZLdk+wAPBNYOW+ZlcDz2vRTgc9W1XojZJIkSduyqY2QtXPCDgPOZPjZi/dU1WVJjgZWV9VK4N3AyUnWMIyMPXNa9ZEkSVqspvo7ZFW1Clg1r+zIken/Bp42zTpsAV0OlS4Stn022fbZZNtn1yy3f9G0PR4hlCRJ6strWUqSJHVmIJMkSerMQLaAJFcnuSTJhUlW967PtCV5T5JvJbl0pGynJJ9K8rX2/2496zgtC7T9qCT/0fr/wiRP7FnHaUiyW5KzklyR5LIkL2vls9LvC7V/Fvp+xyTnJbmotf0vWvnuSb7Y+v5D7Rvy25QNtP29Sb4+0u979q7rtCTZLskFST7e5rf5fp8zpu2Lpt8NZBu2f1XtuVh+o2TK3gscOK/sCOAzVbUc+Eyb3xa9l/XbDnBc6/892xdUtjU3Aa+sqgcBDwde0q43Oyv9vlD7Ydvv+x8Dj62qXwf2BA5M8nCG6wkf1/r+OobrDW9rFmo7wKtG+v3CflWcupcBV4zMz0K/z5nfdlgk/W4gEwBVdQ7r/yjv6LVGTwKevFUrtZUs0PZtXlV9s6q+3Ka/z/AitQuz0+8LtX+bV4MftNnt218Bj2W4rjBso32/gbbPhCS7Ak8C3tXmwwz0O6zf9sXGQLawAv45yZfapZtm0S9V1TdhePMC7tG5PlvbYUkuboc0t8nDdnOSLAP2Ar7IDPb7vPbDDPR9O3RzIfAt4FPAvwHfraqb2iJr2UYD6vy2V9Vcv7+x9ftxSW7bsYrT9FbgT4Gftfm7MyP9zvptn7Mo+t1AtrB9q2pv4AkMhzIe3btC2qr+D3BfhkMa3wT+pm91pifJHYEPA4dX1fW967O1jWn/TPR9Vf20qvZkuKzdPsCDxi22dWu1dcxve5IHA68BHgg8DNgJeHXHKk5Fkt8GvlVVXxotHrPoNtfvC7QdFlG/G8gWUFXXtv/fAj7C8II1a/4zyT0B2v9vda7PVlNV/9letH8GnMg22v9JtmcII/9QVf/Yimem38e1f1b6fk5VfRc4m+E8urtmuK4wjL/+8DZlpO0HtkPYVVU/Bv6ebbPf9wUOSnI1cArDocq3Mhv9vl7bk7x/MfW7gWyMJHdIcqe5aeC3gEs3vNY2afRao88D/qljXbaquUDSPIVtsP/buSPvBq6oqreM3DQT/b5Q+2ek75cmuWubvh1wAMM5dGcxXFcYttG+X6DtXxn5EBKGc6i2uX6vqtdU1a5VtYzhUoWfrapnMQP9vkDbn72Y+n2ql066Ffsl4CND/7AE+EBVfbJvlaYryQeB/YCdk6wF/hw4Bjg1yQuAb7D4L3O1WRZo+37t688FXA38QbcKTs++wHOAS9r5NAB/xoz0Owu3/5AZ6Pt7Aicl2Y7hg/mpVfXxJJcDpyR5A3ABQ2Dd1izU9s8mWcpwCO9C4MU9K7mVvZptv98X8g+Lpd+9dJIkSVJnHrKUJEnqzEAmSZLUmYFMkiSpMwOZJElSZwYySZKkzgxkukWS/DTJhUkuTXJakttvxjYO38z1jk5ywKaut8C2np9kXWvLV5K8fOS2o5JUkvuNlL28la1o81cn2Xnk9v2SfHwj97ksyf/cEvXfkpIclmRNa99om5Lk7e22i5PsvcD6Bya5si13xEj57km+mORrST6UZIdWfts2v6bdvmzabdwcSZ6cmy8+vinr/WCCZcbu8zHLvSnJZUmuaH2RVn5Ikktav3xybhtJjm1l7xvZxnOSvGxT2zFtSc6eez7d2iR5SJIvtL65JMmOrXyHJCck+Wp7Xfm9SddPcqf2ejT39+0kb23L/3F7zV018jx6ZJK3jNu+bh0MZLqlbqiqPavqwcCNbN5vuBwObFIgS7JdVR1ZVZ/elHU2ssiH2uVU9gVem2S3kdsuYfgxwTlPBS6fuMLjLQPGBrLc/KvZPXye4ccy/31e+ROA5e3vUIZLDP2Cto+Pb8vuwfCbXnMh5ljguKpaDlwHvKCVvwC4rqruBxzXlluMnszQpmlYaJ//XJLfZHhsPgR4MMOlXh7THitvA/avqocAFzNci/MuwG+2su2S/FqGH0J9PvC3U2pHFz2fL+2+3w+8uKp+leE3DX/Sbn4tw+V67s/w2PncpOtX1ffba+ue7XXp34G5q2m8kOFxcAHwP1ow/9/A66fTSm0NBjJtSf8C3A8gySvaJ7hLkxzeyu6Q5IwkF7XyZyR5KfArwFlJzmrL/Vb7tPjlDKNud2zlVyc5Msm/Ak9L8t4kT223PS7JBe3T5XvSLhA7f51JGlFV3wHWMPyA5JyPAge3bd4H+B6w7hbur2OAR7VPvy/PMEp3WpKPMVzY/o5JPtP2wyVJDp5bMclz28jHRUlObmVLk3w4yfntb99W/piRT9kXpF2FYgPtv6Cqrh5z08HA+9plRs5luNzKPectsw+wpqquqqobGS5RcnB7w3gscHpb7iSGgDO33ZPa9OnA4+ZGfhaS5KNJvtRGFA4dKT+w7a+Lknymld0xyd+PjCD9Xivf0OPs2CTntb/7tTB0EPDmth/v2/4+2erxL0ke2NbfvW33/CQTvUFuYJ//wmLAjsAOwG2B7YH/ZPhBywB3aPvtzgyXvvkZsEMrux1DSHgV8Paq+sn6m19vH6/3fG3lR7a2XZph9GdulO7sDBdnPifDCN7DkvxjhhHRN7RllmUYKTqp9cXpGTM6vlDfzFvm7CR/meRzwMs28Pg/KsmfjKx3aavHQu17aJLPtX49c8xjfL7fAi6uqotgeP2oqp+22/4X8Fet/GdV9e1NXH+uzsuBezC8xs7ZnuGD7E8YfuB4VVVdt5G6ajGrKv/82+w/4Aft/xKGy238IfBQhhGlOwB3BC4D9gJ+DzhxZN27tP9XAzu36Z2Bc4A7tPlXA0eOLPenI+u/l2GkakfgGuD+rfx9DBeKXm+dDbTj+cA72vS9GH6xecc2fxTwJwyfTh/M8Kn3eQzXwFsxcj+XtPUuZAh0H9/Ife43ukyrw1pgp5F9eueR/bKG4Y33V4ErR/bZ3PIfAB450oYr2vTHgH3b9B2BJW36wo3U7+f90uY/Prf9Nv+ZufaPlD0VeNfI/HOAd8zVf6R8N+DSNn0psOvIbf82er8L1G2uzbdr698dWNoeB7vPW+ZY4K0j696NjT/OXtumnzvXR7TH27z2L2/Tv8FwKRYYLj313Db9EtpzZHP2+Zjb/xr4LsMHgjfO2+/XM1wM/Rxgu1b+pwyPx79h+IDxsU14bi/0fN1ppOxk4Hfa9NnAsW36ZQyh8J4M4XFt66NlDMFy7vH4HuBPRtZfsaG+mVe/s4G/HZlf6PF/1Nx9jDzelo1rH0PI+b/A0lb2DOA9bfrFDKNY8+txeNsPZwJfpr3eAHdleDy+pZWfBvzSpOvPW+ZI4K/nPa8uYBhZuxPDY3H7SfvWv8X55wiZbqnbZbjszGqGy+y8G3gk8JGq+mFV/YAhyDyKIbAc0EYfHlVV3xuzvYczDO1/vm33ecC9R27/0Jh1HgB8vaq+2uZPAh69kXXGeUaSy4CrgLdV1X/Pu/0UhsOWT2a44Px8+9fNhxdeOOF9zvepqvqvNh3gL5NcDHwa2IXhsl6PBU6v9ml7ZPkDgHe0/bYSuHMbDfs88JYMo5F3raqb2np7bmLdxo1azb/Ux0LLbGjdSbY730uTXAScyxDuljM8ds6pqq/Devvl+J9veBhF2Njj7IMj/x8x/87biM1vAqe19d/JzSOq+46sf/IvNGrT9/nofd4PeBDDxZ93Ybg48qMzXCD9Dxk+9PwKwyHL17T7e1N7TL6S4XDWkUlemOTUJK/byF0u9HzdP8O5fpcwPBZ/dWSdlSPrXlbDhZt/zPCcmjsF4Jqq+nybfj/D68WojfXNqNHn9kKP/01p3wMYPnR9qm3ndQz7m6r6u6r6uzHbWdLa8Kz2/ylJHtfKdwU+X1V7A19gCNSTrj/qmdz8mKKqTq6qvarq2cArgLcDT2gjjscl8b39VshrWeqWumH+m8zcIYz5quqrSR4KPBH4qyT/XFVHz1ssDKHkkAXu74djyjZ4eGuBdcb5UFUdluQRwBlJPlFV/2/k9o8BbwZWV9X1CzTzlhqt67MYRn0eWlU/SXI1w2hgGB9YbgM8oqpumFd+TJIzGPb7uUkOqKqvbEbd1nLzmyoMbzbXTrjMtxkOcS5pgXB03bl11mY4n+YuwH+xgCT7Mbz5PqKqfpTkbDa8X8aVb+xxVgtMz7kN8N0NBKxpXJPuKcC57UMOST7BEF5uAKiqf2vlpwJHjK6YZK82+VWGDxuPTnJKkuVV9bWxDRjzfAXexHD+2YqquibJUQz7fs6P2/+fjUzPzc+938zfN5vaN6NGny9jH/9JbuIXT8/ZERZs30cYguR6IXwD1gKfm/uAlGQVsDfwWeBH3Pzh7TRuPm9ykvXnDrn/OsOo9pfmr5jkV4CHVdVfJDmP4cPDG4HHAZ/ahDZoETBFaxrOAZ6c5PZJ7sDwRvIv7cXjR1X1foZPinPf0vs+w7A7DCMe+7bRANo27r+R+/sKsCw3fwvyOYw5ebZt77Akh21oY1X1BYaRjZfNK7+B4fDJGzdSn/n3uU9GvuU2YrTd49yF4YTgnyTZn5tHCT4DPD3J3dv2d2rl/wz8vG0ZLpBNkvtW1SVVdSzDSOYDN6X+I1YCz83g4cD3quqb7T7mAt75wPIM51HtwPDJfmVVFXAWw6E1GEY9/mlku89r009lOPRXSXZJOw9szH65roWxBzKEEhhGIB6TZPeN7Je7sfHH2TNG/n+hTf+8v6rqeuDrSZ7W1k9744RhRHLuCyDPGlP/zfUN2kn8bVTsMcAVwH8Ae2S4QDLA41v5qNczHPbaHpj7csvPgNsvtJ8XeL7Oha9vt1HCp85fbwL3ah96AA4B/nXe7ZvzGgALPP4ZDgPv3cr2BuYeH+PadyWwdK5+SbZPMjoCOM6ZwENaPZcw9Mvl7TH/MYZTE2AISeO+CDR2/ZHbD2FkdGye1zOczA/D4fui9etG6qxFyECmLa6qvsxwvs15wBcZzim6APg14Lx2KOC1wBvaKicAn0hyVlWtYziX6oPtUN25bCRAtEOLv89w+OgShhekcYcWaNv6zgTNOBb4/fmHPKrqlNa+TXEv2ijGPBcDN2U4qfjlY27/B2BFktUMb+xfaXW4jCEUfq4dtpv7qvtL2/IXJ7mcm7/xeniGk5YvavX4BEDrh/UkeWmStQyjWBcneVe7aRXDoac1wInAH7Xld6aNUrbRr8MY3mSuAE5t9YUhzL4iyRqG84ne3crfDdy9lb+Cm0d37gncNKaKnwSWtMfH6xkeI7THzqHAP7a2zh3OegNwt5F9sP8Ej7PbJvkiQyif65tTgFdl+GLEfRn65AVtm5fRvvTR1nlJkvMZwuPovt2kfZ5kxcj+P53h/LpLgIuAi6rqY1V1LfAXwDmtLXsCfzmy7ScD51fVtVX1XeAL7XlSNZxIvtB+Xu/52tY/sdXhowwBfFNdATyv1XUn5n1bd3NeA5qFHv8fBnZq7fhDhlHChdp3I0PIPLb164UMh6ZJ8uIk632LvB0CfwvDvrgQ+HJVndFufjVwVGvHc4BXtm0dlOToCdYHeDpjAlnaqGd7bYXheXQJQ7D85AT7S4tMhhAvzYYMvw32u+01TD8PAAAAd0lEQVSFd2vd55uBk6vq4q11n1tTkt8G7lNVb9/C2z0M+EZVrdzowlv2fq9mOCQ37htx25ytuZ8z/Mbcx2v4mRxJIwxkkjRi1gLZ1mQgkxZmIJMkSerMc8gkSZI6M5BJkiR1ZiCTJEnqzEAmSZLUmYFMkiSps/8Pme930ZXQ30oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "posterior_third.plot_histogram(show=True, bins=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## now test with LSTM\n",
    "but we need to use a slightly different model because LSTM won't work with exponential distribution.  Instead we will use a normal distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "class my_model_normal(Model):\n",
    "    def __init__(self, ymean, xmax, xs):\n",
    "        super().__init__(name='my_experiment') # give the model a name\n",
    "        self.prior_mean = ymean\n",
    "        self.xmax = xmax\n",
    "        self.prior_std = 1\n",
    "        self.likelihood_std = 1\n",
    "        self.xs = xs\n",
    "\n",
    "    def forward(self): # Needed to specifcy how the generative model is run forward\n",
    "        # doesn't work with expnential, so use normal.\n",
    "        mu1 = pyprob.sample(Normal(self.prior_mean, self.prior_std)) # NOTE: sample -> denotes latent variables\n",
    "        mu2 = pyprob.sample(Normal(self.prior_mean, self.prior_std)) # NOTE: sample -> denotes latent variables\n",
    "        tau = pyprob.sample(Uniform(0,self.xmax))\n",
    "        \n",
    "        for i, x in enumerate(self.xs):\n",
    "            if tau.numpy() > x:\n",
    "                mu = mu2\n",
    "            else:\n",
    "                mu = mu1\n",
    "            likelihood = Normal(mu, self.likelihood_std)\n",
    "            pyprob.observe(likelihood, name='obs'+str(i))\n",
    "\n",
    "        # return the latent quantity of interest\n",
    "        #return mu1, mu2, tau\n",
    "        return mu1, mu2 , tau\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = my_model_normal(ymean, len(xs), xs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "observemb = {}\n",
    "for i in range(74):\n",
    "    observemb[\"obs\"+str(i)] = {'dim' : 32}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating new inference network...\n",
      "Observable obs0: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs0: using embedding dim torch.Size([32]).\n",
      "Observable obs0: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs0: embedding depth not specified, using the default 2.\n",
      "Observable obs1: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs1: using embedding dim torch.Size([32]).\n",
      "Observable obs1: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs1: embedding depth not specified, using the default 2.\n",
      "Observable obs2: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs2: using embedding dim torch.Size([32]).\n",
      "Observable obs2: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs2: embedding depth not specified, using the default 2.\n",
      "Observable obs3: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs3: using embedding dim torch.Size([32]).\n",
      "Observable obs3: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs3: embedding depth not specified, using the default 2.\n",
      "Observable obs4: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs4: using embedding dim torch.Size([32]).\n",
      "Observable obs4: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs4: embedding depth not specified, using the default 2.\n",
      "Observable obs5: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs5: using embedding dim torch.Size([32]).\n",
      "Observable obs5: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs5: embedding depth not specified, using the default 2.\n",
      "Observable obs6: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs6: using embedding dim torch.Size([32]).\n",
      "Observable obs6: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs6: embedding depth not specified, using the default 2.\n",
      "Observable obs7: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs7: using embedding dim torch.Size([32]).\n",
      "Observable obs7: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs7: embedding depth not specified, using the default 2.\n",
      "Observable obs8: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs8: using embedding dim torch.Size([32]).\n",
      "Observable obs8: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs8: embedding depth not specified, using the default 2.\n",
      "Observable obs9: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs9: using embedding dim torch.Size([32]).\n",
      "Observable obs9: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs9: embedding depth not specified, using the default 2.\n",
      "Observable obs10: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs10: using embedding dim torch.Size([32]).\n",
      "Observable obs10: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs10: embedding depth not specified, using the default 2.\n",
      "Observable obs11: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs11: using embedding dim torch.Size([32]).\n",
      "Observable obs11: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs11: embedding depth not specified, using the default 2.\n",
      "Observable obs12: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs12: using embedding dim torch.Size([32]).\n",
      "Observable obs12: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs12: embedding depth not specified, using the default 2.\n",
      "Observable obs13: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs13: using embedding dim torch.Size([32]).\n",
      "Observable obs13: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs13: embedding depth not specified, using the default 2.\n",
      "Observable obs14: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs14: using embedding dim torch.Size([32]).\n",
      "Observable obs14: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs14: embedding depth not specified, using the default 2.\n",
      "Observable obs15: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs15: using embedding dim torch.Size([32]).\n",
      "Observable obs15: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs15: embedding depth not specified, using the default 2.\n",
      "Observable obs16: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs16: using embedding dim torch.Size([32]).\n",
      "Observable obs16: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs16: embedding depth not specified, using the default 2.\n",
      "Observable obs17: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs17: using embedding dim torch.Size([32]).\n",
      "Observable obs17: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs17: embedding depth not specified, using the default 2.\n",
      "Observable obs18: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs18: using embedding dim torch.Size([32]).\n",
      "Observable obs18: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs18: embedding depth not specified, using the default 2.\n",
      "Observable obs19: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs19: using embedding dim torch.Size([32]).\n",
      "Observable obs19: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs19: embedding depth not specified, using the default 2.\n",
      "Observable obs20: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs20: using embedding dim torch.Size([32]).\n",
      "Observable obs20: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs20: embedding depth not specified, using the default 2.\n",
      "Observable obs21: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs21: using embedding dim torch.Size([32]).\n",
      "Observable obs21: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs21: embedding depth not specified, using the default 2.\n",
      "Observable obs22: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs22: using embedding dim torch.Size([32]).\n",
      "Observable obs22: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs22: embedding depth not specified, using the default 2.\n",
      "Observable obs23: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs23: using embedding dim torch.Size([32]).\n",
      "Observable obs23: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs23: embedding depth not specified, using the default 2.\n",
      "Observable obs24: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs24: using embedding dim torch.Size([32]).\n",
      "Observable obs24: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs24: embedding depth not specified, using the default 2.\n",
      "Observable obs25: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs25: using embedding dim torch.Size([32]).\n",
      "Observable obs25: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs25: embedding depth not specified, using the default 2.\n",
      "Observable obs26: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs26: using embedding dim torch.Size([32]).\n",
      "Observable obs26: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs26: embedding depth not specified, using the default 2.\n",
      "Observable obs27: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs27: using embedding dim torch.Size([32]).\n",
      "Observable obs27: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs27: embedding depth not specified, using the default 2.\n",
      "Observable obs28: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs28: using embedding dim torch.Size([32]).\n",
      "Observable obs28: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs28: embedding depth not specified, using the default 2.\n",
      "Observable obs29: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs29: using embedding dim torch.Size([32]).\n",
      "Observable obs29: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs29: embedding depth not specified, using the default 2.\n",
      "Observable obs30: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs30: using embedding dim torch.Size([32]).\n",
      "Observable obs30: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs30: embedding depth not specified, using the default 2.\n",
      "Observable obs31: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs31: using embedding dim torch.Size([32]).\n",
      "Observable obs31: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs31: embedding depth not specified, using the default 2.\n",
      "Observable obs32: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs32: using embedding dim torch.Size([32]).\n",
      "Observable obs32: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs32: embedding depth not specified, using the default 2.\n",
      "Observable obs33: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs33: using embedding dim torch.Size([32]).\n",
      "Observable obs33: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs33: embedding depth not specified, using the default 2.\n",
      "Observable obs34: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs34: using embedding dim torch.Size([32]).\n",
      "Observable obs34: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs34: embedding depth not specified, using the default 2.\n",
      "Observable obs35: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs35: using embedding dim torch.Size([32]).\n",
      "Observable obs35: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs35: embedding depth not specified, using the default 2.\n",
      "Observable obs36: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs36: using embedding dim torch.Size([32]).\n",
      "Observable obs36: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs36: embedding depth not specified, using the default 2.\n",
      "Observable obs37: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs37: using embedding dim torch.Size([32]).\n",
      "Observable obs37: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs37: embedding depth not specified, using the default 2.\n",
      "Observable obs38: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs38: using embedding dim torch.Size([32]).\n",
      "Observable obs38: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs38: embedding depth not specified, using the default 2.\n",
      "Observable obs39: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs39: using embedding dim torch.Size([32]).\n",
      "Observable obs39: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs39: embedding depth not specified, using the default 2.\n",
      "Observable obs40: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs40: using embedding dim torch.Size([32]).\n",
      "Observable obs40: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs40: embedding depth not specified, using the default 2.\n",
      "Observable obs41: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs41: using embedding dim torch.Size([32]).\n",
      "Observable obs41: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs41: embedding depth not specified, using the default 2.\n",
      "Observable obs42: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs42: using embedding dim torch.Size([32]).\n",
      "Observable obs42: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs42: embedding depth not specified, using the default 2.\n",
      "Observable obs43: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs43: using embedding dim torch.Size([32]).\n",
      "Observable obs43: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs43: embedding depth not specified, using the default 2.\n",
      "Observable obs44: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs44: using embedding dim torch.Size([32]).\n",
      "Observable obs44: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs44: embedding depth not specified, using the default 2.\n",
      "Observable obs45: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs45: using embedding dim torch.Size([32]).\n",
      "Observable obs45: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs45: embedding depth not specified, using the default 2.\n",
      "Observable obs46: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs46: using embedding dim torch.Size([32]).\n",
      "Observable obs46: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs46: embedding depth not specified, using the default 2.\n",
      "Observable obs47: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs47: using embedding dim torch.Size([32]).\n",
      "Observable obs47: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs47: embedding depth not specified, using the default 2.\n",
      "Observable obs48: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs48: using embedding dim torch.Size([32]).\n",
      "Observable obs48: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs48: embedding depth not specified, using the default 2.\n",
      "Observable obs49: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs49: using embedding dim torch.Size([32]).\n",
      "Observable obs49: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs49: embedding depth not specified, using the default 2.\n",
      "Observable obs50: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs50: using embedding dim torch.Size([32]).\n",
      "Observable obs50: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs50: embedding depth not specified, using the default 2.\n",
      "Observable obs51: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs51: using embedding dim torch.Size([32]).\n",
      "Observable obs51: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs51: embedding depth not specified, using the default 2.\n",
      "Observable obs52: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs52: using embedding dim torch.Size([32]).\n",
      "Observable obs52: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs52: embedding depth not specified, using the default 2.\n",
      "Observable obs53: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs53: using embedding dim torch.Size([32]).\n",
      "Observable obs53: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs53: embedding depth not specified, using the default 2.\n",
      "Observable obs54: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs54: using embedding dim torch.Size([32]).\n",
      "Observable obs54: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs54: embedding depth not specified, using the default 2.\n",
      "Observable obs55: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs55: using embedding dim torch.Size([32]).\n",
      "Observable obs55: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs55: embedding depth not specified, using the default 2.\n",
      "Observable obs56: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs56: using embedding dim torch.Size([32]).\n",
      "Observable obs56: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs56: embedding depth not specified, using the default 2.\n",
      "Observable obs57: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs57: using embedding dim torch.Size([32]).\n",
      "Observable obs57: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs57: embedding depth not specified, using the default 2.\n",
      "Observable obs58: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs58: using embedding dim torch.Size([32]).\n",
      "Observable obs58: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs58: embedding depth not specified, using the default 2.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Observable obs59: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs59: using embedding dim torch.Size([32]).\n",
      "Observable obs59: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs59: embedding depth not specified, using the default 2.\n",
      "Observable obs60: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs60: using embedding dim torch.Size([32]).\n",
      "Observable obs60: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs60: embedding depth not specified, using the default 2.\n",
      "Observable obs61: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs61: using embedding dim torch.Size([32]).\n",
      "Observable obs61: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs61: embedding depth not specified, using the default 2.\n",
      "Observable obs62: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs62: using embedding dim torch.Size([32]).\n",
      "Observable obs62: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs62: embedding depth not specified, using the default 2.\n",
      "Observable obs63: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs63: using embedding dim torch.Size([32]).\n",
      "Observable obs63: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs63: embedding depth not specified, using the default 2.\n",
      "Observable obs64: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs64: using embedding dim torch.Size([32]).\n",
      "Observable obs64: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs64: embedding depth not specified, using the default 2.\n",
      "Observable obs65: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs65: using embedding dim torch.Size([32]).\n",
      "Observable obs65: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs65: embedding depth not specified, using the default 2.\n",
      "Observable obs66: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs66: using embedding dim torch.Size([32]).\n",
      "Observable obs66: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs66: embedding depth not specified, using the default 2.\n",
      "Observable obs67: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs67: using embedding dim torch.Size([32]).\n",
      "Observable obs67: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs67: embedding depth not specified, using the default 2.\n",
      "Observable obs68: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs68: using embedding dim torch.Size([32]).\n",
      "Observable obs68: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs68: embedding depth not specified, using the default 2.\n",
      "Observable obs69: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs69: using embedding dim torch.Size([32]).\n",
      "Observable obs69: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs69: embedding depth not specified, using the default 2.\n",
      "Observable obs70: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs70: using embedding dim torch.Size([32]).\n",
      "Observable obs70: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs70: embedding depth not specified, using the default 2.\n",
      "Observable obs71: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs71: using embedding dim torch.Size([32]).\n",
      "Observable obs71: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs71: embedding depth not specified, using the default 2.\n",
      "Observable obs72: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs72: using embedding dim torch.Size([32]).\n",
      "Observable obs72: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs72: embedding depth not specified, using the default 2.\n",
      "Observable obs73: reshape not specified, using shape torch.Size([]).\n",
      "Observable obs73: using embedding dim torch.Size([32]).\n",
      "Observable obs73: observe embedding not specified, using the default FEEDFORWARD.\n",
      "Observable obs73: embedding depth not specified, using the default 2.\n",
      "Observe embedding dimension: 2368\n",
      "Train. time | Epoch| Trace     | Init. loss| Min. loss | Curr. loss| T.since min | Learn.rate| Traces/sec\n",
      "New layers, address: 16__forward__mu1__Normal__1, distribution: Normal\n",
      "New layers, address: 36__forward__mu2__Normal__1, distribution: Normal\n",
      "New layers, address: 54__forward__tau__Uniform__1, distribution: Uniform\n",
      "Total addresses: 3, distribution types: 2, parameters: 17,909,429\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0d:00:02:56 | 1    | 7,232     | +7.03e+00 | +6.87e+00 | +7.03e+00 | 0d:00:00:00 | +1.00e-03 | 69.5 +7.03e+00 | +7.44e+00 | 0d:00:00:00 | +1.00e-03 | 46.2 +7.28e+00 | 0d:00:00:02 | +1.00e-03 | 45.7                               +7.13e+00 | 0d:00:00:04 | +1.00e-03 | 49.7                               +7.03e+00 | +7.03e+00 | 0d:00:00:00 | +1.00e-03 | 44.7 +7.03e+00 | 0d:00:00:01 | +1.00e-03 | 42.7                               +7.23e+00 | 0d:00:00:03 | +1.00e-03 | 33.8                               +7.07e+00 | 0d:00:00:05 | +1.00e-03 | 31.5                               +7.12e+00 | 0d:00:00:07 | +1.00e-03 | 29.8                               +7.06e+00 | 0d:00:00:09 | +1.00e-03 | 37.4                               +7.08e+00 | 0d:00:00:11 | +1.00e-03 | 37.1                               +7.06e+00 | 0d:00:00:12 | +1.00e-03 | 43.2                               +7.17e+00 | 0d:00:00:13 | +1.00e-03 | 44.1                               +7.37e+00 | 0d:00:00:15 | +1.00e-03 | 47.1                               +7.24e+00 | 0d:00:00:16 | +1.00e-03 | 47.2                               +7.13e+00 | 0d:00:00:18 | +1.00e-03 | 45.9                               +7.05e+00 | 0d:00:00:19 | +1.00e-03 | 49.0                               +7.06e+00 | 0d:00:00:20 | +1.00e-03 | 48.3                               +7.04e+00 | 0d:00:00:21 | +1.00e-03 | 50.3                               +6.93e+00 | +6.93e+00 | 0d:00:00:00 | +1.00e-03 | 45.8 +7.25e+00 | 0d:00:00:01 | +1.00e-03 | 47.6                               +7.24e+00 | 0d:00:00:02 | +1.00e-03 | 45.0                               +7.22e+00 | 0d:00:00:04 | +1.00e-03 | 50.4                               +7.18e+00 | 0d:00:00:05 | +1.00e-03 | 48.0                               +7.19e+00 | 0d:00:00:06 | +1.00e-03 | 47.0                               +7.38e+00 | 0d:00:00:08 | +1.00e-03 | 48.5                               +7.09e+00 | 0d:00:00:09 | +1.00e-03 | 48.0                               +7.22e+00 | 0d:00:00:10 | +1.00e-03 | 47.0                               +7.13e+00 | 0d:00:00:12 | +1.00e-03 | 45.3                               +7.23e+00 | 0d:00:00:13 | +1.00e-03 | 47.4                               +7.11e+00 | 0d:00:00:14 | +1.00e-03 | 46.2                               +7.06e+00 | 0d:00:00:16 | +1.00e-03 | 33.6                               +7.17e+00 | 0d:00:00:19 | +1.00e-03 | 28.6                               +7.06e+00 | 0d:00:00:20 | +1.00e-03 | 43.5                               +7.16e+00 | 0d:00:00:21 | +1.00e-03 | 44.8                               +6.96e+00 | 0d:00:00:23 | +1.00e-03 | 49.5                               +7.05e+00 | 0d:00:00:24 | +1.00e-03 | 39.3                               +6.95e+00 | 0d:00:00:26 | +1.00e-03 | 32.1                               +6.97e+00 | 0d:00:00:28 | +1.00e-03 | 38.1                               +7.13e+00 | 0d:00:00:30 | +1.00e-03 | 37.6                               +7.27e+00 | 0d:00:00:32 | +1.00e-03 | 35.6                               +6.96e+00 | 0d:00:00:33 | +1.00e-03 | 33.9                               +7.32e+00 | 0d:00:00:35 | +1.00e-03 | 39.5                               +7.14e+00 | 0d:00:00:37 | +1.00e-03 | 40.1                               +7.48e+00 | 0d:00:00:37 | +1.00e-03 | 41.8                           +7.44e+00 | 0d:00:00:40 | +1.00e-03 | 36.3                               +7.08e+00 | 0d:00:00:42 | +1.00e-03 | 37.0                               +7.05e+00 | 0d:00:00:43 | +1.00e-03 | 38.3                               +7.12e+00 | 0d:00:00:45 | +1.00e-03 | 38.6                               +7.24e+00 | 0d:00:00:47 | +1.00e-03 | 34.7                               +7.23e+00 | 0d:00:00:48 | +1.00e-03 | 38.4                               +6.99e+00 | 0d:00:00:50 | +1.00e-03 | 36.6                               +7.28e+00 | 0d:00:00:52 | +1.00e-03 | 37.8                               +7.11e+00 | 0d:00:00:54 | +1.00e-03 | 38.4                               +7.10e+00 | 0d:00:00:55 | +1.00e-03 | 36.2                               +7.18e+00 | 0d:00:00:57 | +1.00e-03 | 38.9                               +7.18e+00 | 0d:00:00:58 | +1.00e-03 | 44.7                               +7.17e+00 | 0d:00:01:00 | +1.00e-03 | 45.7                               +7.10e+00 | 0d:00:01:01 | +1.00e-03 | 44.4                               +7.11e+00 | 0d:00:01:03 | +1.00e-03 | 41.7                               +7.02e+00 | 0d:00:01:04 | +1.00e-03 | 43.0                               +7.25e+00 | 0d:00:01:06 | +1.00e-03 | 42.0                               +7.29e+00 | 0d:00:01:08 | +1.00e-03 | 37.7                               +6.96e+00 | 0d:00:01:09 | +1.00e-03 | 44.4                               +7.30e+00 | 0d:00:01:10 | +1.00e-03 | 44.0                               +7.09e+00 | 0d:00:01:12 | +1.00e-03 | 32.4                               +7.04e+00 | 0d:00:01:14 | +1.00e-03 | 33.9                               +7.13e+00 | 0d:00:01:16 | +1.00e-03 | 33.9                               +7.14e+00 | 0d:00:01:18 | +1.00e-03 | 35.4                               +6.93e+00 | 0d:00:01:20 | +1.00e-03 | 41.8                               +7.13e+00 | 0d:00:01:21 | +1.00e-03 | 45.4                               +7.30e+00 | 0d:00:01:22 | +1.00e-03 | 45.8                               +7.16e+00 | 0d:00:01:24 | +1.00e-03 | 46.0                               +6.87e+00 | +6.87e+00 | 0d:00:00:00 | +1.00e-03 | 43.7 +7.29e+00 | 0d:00:00:01 | +1.00e-03 | 46.2                               +7.03e+00 | 0d:00:00:03 | +1.00e-03 | 36.4                               +7.03e+00 | 0d:00:00:04 | +1.00e-03 | 39.2                               +7.20e+00 | 0d:00:00:06 | +1.00e-03 | 44.2                               +6.96e+00 | 0d:00:00:07 | +1.00e-03 | 41.3                               +7.07e+00 | 0d:00:00:09 | +1.00e-03 | 40.7                               +7.07e+00 | 0d:00:00:10 | +1.00e-03 | 40.3                               +7.08e+00 | 0d:00:00:12 | +1.00e-03 | 42.3                               +7.13e+00 | 0d:00:00:13 | +1.00e-03 | 41.8                               +7.18e+00 | 0d:00:00:15 | +1.00e-03 | 44.0                               +7.18e+00 | 0d:00:00:16 | +1.00e-03 | 42.7                               +7.17e+00 | 0d:00:00:18 | +1.00e-03 | 44.3                               +7.28e+00 | 0d:00:00:19 | +1.00e-03 | 42.9                               +7.00e+00 | 0d:00:00:21 | +1.00e-03 | 38.8                               +7.17e+00 | 0d:00:00:23 | +1.00e-03 | 33.2                               +7.09e+00 | 0d:00:00:25 | +1.00e-03 | 34.1                               +7.20e+00 | 0d:00:00:27 | +1.00e-03 | 37.7                               +7.22e+00 | 0d:00:00:28 | +1.00e-03 | 41.9                               +6.98e+00 | 0d:00:00:29 | +1.00e-03 | 44.6                               +7.07e+00 | 0d:00:00:31 | +1.00e-03 | 43.2                               +7.01e+00 | 0d:00:00:32 | +1.00e-03 | 44.0                               +7.20e+00 | 0d:00:00:34 | +1.00e-03 | 42.5                               +7.27e+00 | 0d:00:00:35 | +1.00e-03 | 46.1                               +6.90e+00 | 0d:00:00:37 | +1.00e-03 | 42.3                               +7.06e+00 | 0d:00:00:38 | +1.00e-03 | 43.1                               +7.26e+00 | 0d:00:00:40 | +1.00e-03 | 44.4                               +7.40e+00 | 0d:00:00:41 | +1.00e-03 | 44.7                               +7.22e+00 | 0d:00:00:43 | +1.00e-03 | 41.1                               +7.06e+00 | 0d:00:00:44 | +1.00e-03 | 41.8                               +7.09e+00 | 0d:00:00:46 | +1.00e-03 | 43.3                               +7.14e+00 | 0d:00:00:47 | +1.00e-03 | 42.3                               +7.13e+00 | 0d:00:00:49 | +1.00e-03 | 44.9                               +6.98e+00 | 0d:00:00:50 | +1.00e-03 | 40.3                               +7.40e+00 | 0d:00:00:52 | +1.00e-03 | 38.4                               +7.02e+00 | 0d:00:00:53 | +1.00e-03 | 40.9                               +7.09e+00 | 0d:00:00:55 | +1.00e-03 | 41.3                               +7.23e+00 | 0d:00:00:57 | +1.00e-03 | 37.4                               +7.03e+00 | 0d:00:00:58 | +1.00e-03 | 41.6                               +7.13e+00 | 0d:00:01:01 | +1.00e-03 | 27.2                               0d:00:05:46 | 1    | 14,400    | +7.03e+00 | +6.72e+00 | +7.24e+00 | 0d:00:01:03 | +1.00e-03 | 32.2                               +7.17e+00 | 0d:00:01:04 | +1.00e-03 | 36.6                               +7.20e+00 | 0d:00:01:06 | +1.00e-03 | 40.2                               +7.16e+00 | 0d:00:01:08 | +1.00e-03 | 37.5                               +7.17e+00 | 0d:00:01:09 | +1.00e-03 | 36.2                               +7.07e+00 | 0d:00:01:11 | +1.00e-03 | 36.7                               +7.13e+00 | 0d:00:01:13 | +1.00e-03 | 44.0                               +7.16e+00 | 0d:00:01:14 | +1.00e-03 | 42.7                               +7.34e+00 | 0d:00:01:16 | +1.00e-03 | 43.0                               +7.07e+00 | 0d:00:01:17 | +1.00e-03 | 37.1                               +7.15e+00 | 0d:00:01:19 | +1.00e-03 | 42.1                               +7.07e+00 | 0d:00:01:20 | +1.00e-03 | 40.5                               +6.95e+00 | 0d:00:01:22 | +1.00e-03 | 44.0                               +6.72e+00 | +6.72e+00 | 0d:00:00:00 | +1.00e-03 | 44.0 +7.22e+00 | 0d:00:00:01 | +1.00e-03 | 40.9                               +7.07e+00 | 0d:00:00:03 | +1.00e-03 | 41.8                               +7.19e+00 | 0d:00:00:04 | +1.00e-03 | 41.6                               +6.94e+00 | 0d:00:00:06 | +1.00e-03 | 43.2                               +7.14e+00 | 0d:00:00:07 | +1.00e-03 | 46.0                               +7.11e+00 | 0d:00:00:08 | +1.00e-03 | 43.7                               +7.31e+00 | 0d:00:00:10 | +1.00e-03 | 45.8                               +7.06e+00 | 0d:00:00:11 | +1.00e-03 | 44.7                               +7.17e+00 | 0d:00:00:13 | +1.00e-03 | 45.6                               +7.20e+00 | 0d:00:00:14 | +1.00e-03 | 44.0                               +7.24e+00 | 0d:00:00:16 | +1.00e-03 | 42.4                               +7.01e+00 | 0d:00:00:17 | +1.00e-03 | 42.0                               +7.09e+00 | 0d:00:00:19 | +1.00e-03 | 43.7                               +7.13e+00 | 0d:00:00:20 | +1.00e-03 | 41.9                               +7.26e+00 | 0d:00:00:22 | +1.00e-03 | 39.7                               +7.07e+00 | 0d:00:00:24 | +1.00e-03 | 32.4                               +7.06e+00 | 0d:00:00:26 | +1.00e-03 | 33.2                               +7.12e+00 | 0d:00:00:28 | +1.00e-03 | 33.8                               +7.15e+00 | 0d:00:00:29 | +1.00e-03 | 40.2                               +7.07e+00 | 0d:00:00:31 | +1.00e-03 | 44.4                               +7.08e+00 | 0d:00:00:32 | +1.00e-03 | 44.2                               +7.17e+00 | 0d:00:00:34 | +1.00e-03 | 43.7                               +7.00e+00 | 0d:00:00:35 | +1.00e-03 | 38.9                               +7.19e+00 | 0d:00:00:37 | +1.00e-03 | 36.1                               +7.11e+00 | 0d:00:00:38 | +1.00e-03 | 44.9                               +7.29e+00 | 0d:00:00:40 | +1.00e-03 | 46.3                               +7.38e+00 | 0d:00:00:41 | +1.00e-03 | 46.9                               +7.14e+00 | 0d:00:00:43 | +1.00e-03 | 44.1                               +7.26e+00 | 0d:00:00:44 | +1.00e-03 | 48.5                               +7.22e+00 | 0d:00:00:45 | +1.00e-03 | 44.9                               +7.17e+00 | 0d:00:00:47 | +1.00e-03 | 46.4                               +7.16e+00 | 0d:00:00:48 | +1.00e-03 | 42.7                               +7.10e+00 | 0d:00:00:50 | +1.00e-03 | 38.0                               +7.33e+00 | 0d:00:00:51 | +1.00e-03 | 46.6                               +7.14e+00 | 0d:00:00:53 | +1.00e-03 | 48.4                               +7.41e+00 | 0d:00:00:54 | +1.00e-03 | 42.7                               +7.18e+00 | 0d:00:00:56 | +1.00e-03 | 38.0                               +7.06e+00 | 0d:00:00:57 | +1.00e-03 | 38.8                               +7.17e+00 | 0d:00:00:59 | +1.00e-03 | 37.1                               +7.00e+00 | 0d:00:01:00 | +1.00e-03 | 47.0                               +7.00e+00 | 0d:00:01:02 | +1.00e-03 | 47.1                               +7.19e+00 | 0d:00:01:03 | +1.00e-03 | 49.7                               +7.25e+00 | 0d:00:01:05 | +1.00e-03 | 45.3                               +7.23e+00 | 0d:00:01:06 | +1.00e-03 | 40.8                               +7.00e+00 | 0d:00:01:07 | +1.00e-03 | 47.7                               +7.25e+00 | 0d:00:01:09 | +1.00e-03 | 47.8                               +7.10e+00 | 0d:00:01:10 | +1.00e-03 | 50.8                               +7.22e+00 | 0d:00:01:12 | +1.00e-03 | 44.0                               +7.33e+00 | 0d:00:01:13 | +1.00e-03 | 46.5                               +7.23e+00 | 0d:00:01:14 | +1.00e-03 | 42.9                               +7.22e+00 | 0d:00:01:16 | +1.00e-03 | 46.2                               +6.92e+00 | 0d:00:01:17 | +1.00e-03 | 41.7                               +7.06e+00 | 0d:00:01:19 | +1.00e-03 | 47.4                               +7.10e+00 | 0d:00:01:20 | +1.00e-03 | 44.7                               +7.25e+00 | 0d:00:01:22 | +1.00e-03 | 45.2                               +7.31e+00 | 0d:00:01:23 | +1.00e-03 | 43.3                               +7.18e+00 | 0d:00:01:25 | +1.00e-03 | 42.0                               +7.23e+00 | 0d:00:01:26 | +1.00e-03 | 42.3                               +7.22e+00 | 0d:00:01:28 | +1.00e-03 | 40.3                               +7.17e+00 | 0d:00:01:29 | +1.00e-03 | 46.3                               +7.02e+00 | 0d:00:01:30 | +1.00e-03 | 43.2                               +7.14e+00 | 0d:00:01:32 | +1.00e-03 | 46.9                               +7.22e+00 | 0d:00:01:33 | +1.00e-03 | 43.3                               +7.32e+00 | 0d:00:01:35 | +1.00e-03 | 46.5                               +7.35e+00 | 0d:00:01:36 | +1.00e-03 | 42.4                               +7.09e+00 | 0d:00:01:38 | +1.00e-03 | 47.4                               +7.00e+00 | 0d:00:01:39 | +1.00e-03 | 42.9                               +7.20e+00 | 0d:00:01:41 | +1.00e-03 | 35.1                               +7.20e+00 | 0d:00:01:43 | +1.00e-03 | 30.3                               +7.17e+00 | 0d:00:01:45 | +1.00e-03 | 36.0                               +7.01e+00 | 0d:00:01:46 | +1.00e-03 | 43.4                               +6.88e+00 | 0d:00:01:48 | +1.00e-03 | 42.8                               +7.18e+00 | 0d:00:01:49 | +1.00e-03 | 43.4                               +7.07e+00 | 0d:00:01:51 | +1.00e-03 | 44.1                               +7.20e+00 | 0d:00:01:52 | +1.00e-03 | 47.0                               +7.18e+00 | 0d:00:01:53 | +1.00e-03 | 44.3                               +7.21e+00 | 0d:00:01:55 | +1.00e-03 | 47.6                               +7.12e+00 | 0d:00:01:56 | +1.00e-03 | 44.6                               +7.07e+00 | 0d:00:01:58 | +1.00e-03 | 45.1                               +7.11e+00 | 0d:00:01:59 | +1.00e-03 | 42.4                               +6.91e+00 | 0d:00:02:01 | +1.00e-03 | 46.6                               +7.12e+00 | 0d:00:02:02 | +1.00e-03 | 42.9                               +7.08e+00 | 0d:00:02:04 | +1.00e-03 | 41.2                               +7.02e+00 | 0d:00:02:05 | +1.00e-03 | 38.9                               +7.19e+00 | 0d:00:02:07 | +1.00e-03 | 36.0                               +7.28e+00 | 0d:00:02:09 | +1.00e-03 | 37.1                               +7.33e+00 | 0d:00:02:10 | +1.00e-03 | 44.3                               +7.09e+00 | 0d:00:02:12 | +1.00e-03 | 46.6                               +7.05e+00 | 0d:00:02:13 | +1.00e-03 | 43.4                               +7.22e+00 | 0d:00:02:14 | +1.00e-03 | 46.4                               +7.03e+00 | 0d:00:02:16 | +1.00e-03 | 41.4                               +7.24e+00 | 0d:00:02:17 | +1.00e-03 | 45.7                               +7.35e+00 | 0d:00:02:19 | +1.00e-03 | 43.3                               +7.27e+00 | 0d:00:02:20 | +1.00e-03 | 41.9                               +7.07e+00 | 0d:00:02:22 | +1.00e-03 | 36.9                               +7.36e+00 | 0d:00:02:24 | +1.00e-03 | 38.0                               +7.13e+00 | 0d:00:02:25 | +1.00e-03 | 47.4                               +7.08e+00 | 0d:00:02:26 | +1.00e-03 | 47.3                               "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0d:00:07:57 | 1    | 19,968    | +7.03e+00 | +6.72e+00 | +7.13e+00 | 0d:00:02:28 | +1.00e-03 | 49.4                               +7.46e+00 | 0d:00:02:29 | +1.00e-03 | 42.5                               +7.07e+00 | 0d:00:02:31 | +1.00e-03 | 49.7                               +7.08e+00 | 0d:00:02:32 | +1.00e-03 | 47.0                               +7.12e+00 | 0d:00:02:33 | +1.00e-03 | 48.4                               +6.99e+00 | 0d:00:02:35 | +1.00e-03 | 37.1                               +7.17e+00 | 0d:00:02:37 | +1.00e-03 | 35.8                               +7.15e+00 | 0d:00:02:39 | +1.00e-03 | 34.9                               +7.28e+00 | 0d:00:02:40 | +1.00e-03 | 40.2                               +7.07e+00 | 0d:00:02:42 | +1.00e-03 | 47.7                               +7.09e+00 | 0d:00:02:43 | +1.00e-03 | 45.7                               +7.45e+00 | 0d:00:02:44 | +1.00e-03 | 47.0                               +7.17e+00 | 0d:00:02:46 | +1.00e-03 | 43.5                               +7.17e+00 | 0d:00:02:47 | +1.00e-03 | 47.0                               +6.97e+00 | 0d:00:02:49 | +1.00e-03 | 45.9                               +7.06e+00 | 0d:00:02:50 | +1.00e-03 | 47.8                               +7.11e+00 | 0d:00:02:51 | +1.00e-03 | 46.8                               +7.26e+00 | 0d:00:02:53 | +1.00e-03 | 47.8                               +7.26e+00 | 0d:00:02:54 | +1.00e-03 | 46.8                               +6.94e+00 | 0d:00:02:55 | +1.00e-03 | 46.2                               +7.14e+00 | 0d:00:02:57 | +1.00e-03 | 40.3                               +6.94e+00 | 0d:00:02:58 | +1.00e-03 | 45.5                               +7.26e+00 | 0d:00:03:00 | +1.00e-03 | 49.4                               +7.19e+00 | 0d:00:03:01 | +1.00e-03 | 47.1                               +7.12e+00 | 0d:00:03:02 | +1.00e-03 | 44.6                               +7.13e+00 | 0d:00:03:04 | +1.00e-03 | 39.8                               +7.04e+00 | 0d:00:03:06 | +1.00e-03 | 37.5                               +7.08e+00 | 0d:00:03:07 | +1.00e-03 | 36.6                               +7.04e+00 | 0d:00:03:09 | +1.00e-03 | 42.8                               +7.04e+00 | 0d:00:03:11 | +1.00e-03 | 40.1                               +7.13e+00 | 0d:00:03:12 | +1.00e-03 | 43.9                               +7.15e+00 | 0d:00:03:13 | +1.00e-03 | 47.1                               +7.20e+00 | 0d:00:03:15 | +1.00e-03 | 46.2                               +7.31e+00 | 0d:00:03:16 | +1.00e-03 | 49.8                               +6.87e+00 | 0d:00:03:17 | +1.00e-03 | 46.6                               +7.20e+00 | 0d:00:03:19 | +1.00e-03 | 44.7                               +7.09e+00 | 0d:00:03:20 | +1.00e-03 | 44.7                               +7.26e+00 | 0d:00:03:22 | +1.00e-03 | 42.0                               +7.34e+00 | 0d:00:03:23 | +1.00e-03 | 44.3                               +7.05e+00 | 0d:00:03:25 | +1.00e-03 | 30.2                               +7.15e+00 | 0d:00:03:27 | +1.00e-03 | 41.9                               +7.09e+00 | 0d:00:03:28 | +1.00e-03 | 45.8                               +7.25e+00 | 0d:00:03:30 | +1.00e-03 | 44.6                               +7.27e+00 | 0d:00:03:31 | +1.00e-03 | 46.3                               +6.96e+00 | 0d:00:03:35 | +1.00e-03 | 18.9                               +7.04e+00 | 0d:00:03:37 | +1.00e-03 | 26.9                               +7.19e+00 | 0d:00:03:38 | +1.00e-03 | 42.1                               +7.03e+00 | 0d:00:03:41 | +1.00e-03 | 23.6                               +6.94e+00 | 0d:00:03:43 | +1.00e-03 | 27.4                               +7.03e+00 | 0d:00:03:45 | +1.00e-03 | 36.7                               +6.90e+00 | 0d:00:03:47 | +1.00e-03 | 40.7                               +7.15e+00 | 0d:00:03:49 | +1.00e-03 | 36.0                               +6.98e+00 | 0d:00:03:50 | +1.00e-03 | 42.6                               +7.21e+00 | 0d:00:03:51 | +1.00e-03 | 46.1                               +7.02e+00 | 0d:00:03:53 | +1.00e-03 | 47.7                               +7.02e+00 | 0d:00:03:54 | +1.00e-03 | 47.1                               +7.30e+00 | 0d:00:03:56 | +1.00e-03 | 45.0                               +7.21e+00 | 0d:00:03:57 | +1.00e-03 | 48.2                               +7.12e+00 | 0d:00:03:58 | +1.00e-03 | 45.4                               +7.12e+00 | 0d:00:04:00 | +1.00e-03 | 47.0                               +7.15e+00 | 0d:00:04:01 | +1.00e-03 | 45.1                               +7.13e+00 | 0d:00:04:02 | +1.00e-03 | 48.5                               +7.19e+00 | 0d:00:04:04 | +1.00e-03 | 43.7                               +7.06e+00 | 0d:00:04:05 | +1.00e-03 | 46.9                               +7.20e+00 | 0d:00:04:07 | +1.00e-03 | 46.3                               +7.12e+00 | 0d:00:04:08 | +1.00e-03 | 47.7                               +7.11e+00 | 0d:00:04:09 | +1.00e-03 | 45.8                               +7.10e+00 | 0d:00:04:11 | +1.00e-03 | 47.4                               +7.08e+00 | 0d:00:04:12 | +1.00e-03 | 45.9                               +7.23e+00 | 0d:00:04:13 | +1.00e-03 | 45.9                               +7.18e+00 | 0d:00:04:15 | +1.00e-03 | 46.5                               +7.16e+00 | 0d:00:04:16 | +1.00e-03 | 45.1                               +6.92e+00 | 0d:00:04:18 | +1.00e-03 | 48.4                               +6.91e+00 | 0d:00:04:19 | +1.00e-03 | 46.3                               +7.01e+00 | 0d:00:04:20 | +1.00e-03 | 47.0                               +7.24e+00 | 0d:00:04:22 | +1.00e-03 | 46.4                               +7.02e+00 | 0d:00:04:23 | +1.00e-03 | 46.2                               +7.09e+00 | 0d:00:04:25 | +1.00e-03 | 44.8                               +7.22e+00 | 0d:00:04:26 | +1.00e-03 | 48.1                               +7.23e+00 | 0d:00:04:27 | +1.00e-03 | 47.1                               +7.14e+00 | 0d:00:04:29 | +1.00e-03 | 44.4                               +6.96e+00 | 0d:00:04:30 | +1.00e-03 | 47.7                               +7.39e+00 | 0d:00:04:31 | +1.00e-03 | 45.1                               +7.19e+00 | 0d:00:04:33 | +1.00e-03 | 47.5                               +7.07e+00 | 0d:00:04:34 | +1.00e-03 | 43.0                               +7.07e+00 | 0d:00:04:36 | +1.00e-03 | 40.9                               +7.08e+00 | 0d:00:04:38 | +1.00e-03 | 38.4                               \n",
      "Stop condition reached. num_traces: 20000\n",
      "0d:00:07:58 | 1    | 20,032    | +7.03e+00 | +6.72e+00 | +7.27e+00 | 0d:00:04:39 | +1.00e-03 | 47.8                               \n"
     ]
    }
   ],
   "source": [
    "model.learn_inference_network(num_traces=20000,\n",
    "            observe_embeddings=observemb,\n",
    "            inference_network=pyprob.InferenceNetwork.LSTM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time spent  | Time remain.| Progress             | Trace       | Traces/sec\n",
      "0d:00:05:45 | 0d:00:00:00 | #################### | 10000/10000 | 28.97       \n"
     ]
    }
   ],
   "source": [
    "posterior = model.posterior_results(\n",
    "                num_traces=10000, # the number of samples estimating the posterior\n",
    "                inference_engine=pyprob.InferenceEngine.IMPORTANCE_SAMPLING_WITH_INFERENCE_NETWORK, \n",
    "                observe= observdic )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(tensor(22.0710), tensor(18.4651), tensor(43.4458))\n"
     ]
    }
   ],
   "source": [
    "print(posterior.sample())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([22.0705, 18.4650, 43.4460])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior.mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "posterior_first = posterior.map(lambda v: v[2]) # extract var_0\n",
    "var_0_mean = posterior_first.mean\n",
    "posterior_first.plot_histogram(show=True, bins=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "posterior_first = posterior.map(lambda v: v[1]) # extract var_0\n",
    "var_0_mean = posterior_first.mean\n",
    "posterior_first.plot_histogram(show=True, bins=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmEAAAFACAYAAAD07atFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi40LCBodHRwOi8vbWF0cGxvdGxpYi5vcmcv7US4rQAAHbFJREFUeJzt3Xm4ZFV97vHvKy0ogoChTWTQRi/BEExQOsbEWSDBCdTgdE0CUUM0EkVjFKNRrplQiXPuJQjKIEGFoMEZVESSMNhgMwkKUaIduNLGCA4MAX75Y68TD80ZqtuuWqfP+X6e5zy9a9eu2r+1q07Xe9ZetVeqCkmSJE3WPXoXIEmStBQZwiRJkjowhEmSJHVgCJMkSerAECZJktSBIUySJKkDQ5gkSVIHhjBJkqQODGGSJEkdLOtdwCi23377WrFiRe8yJEmS5nXRRRd9t6qWz7fdJhHCVqxYwapVq3qXIUmSNK8k/zbKdp6OlCRJ6sAQJkmS1IEhTJIkqQNDmCRJUgeGMEmSpA4MYZIkSR0YwiRJkjowhEmSJHVgCJMkSerAECZJktSBIUySJKmDTWLuSEmSFoMVh3/ybuuuPfKpHSrRQmBPmCRJUgeGMEmSpA4MYZIkSR0YwiRJkjoYWwhL8v4kNyS5fNq6tyW5KsmlST6aZNtx7V+SJGkhG2dP2PHAfuusOwvYo6p+Cfg68Lox7l+SJGnBGlsIq6ovAd9bZ92ZVXV7u3k+sNO49i9JkrSQ9RwT9kLg07PdmeSQJKuSrFq7du0Ey5IkSRq/LiEsyeuB24GTZ9umqo6pqpVVtXL58uWTK06SJGkCJn7F/CQHAU8D9q6qmvT+JUmSFoKJhrAk+wGvBR5fVT+e5L4lSZIWknFeouIU4DxgtyRrkrwIeC+wNXBWktVJjh7X/iVJkhaysfWEVdXzZ1h93Lj2J0mStCnxivmSJEkdGMIkSZI6MIRJkiR1YAiTJEnqwBAmSZLUgSFMkiSpA0OYJElSB4YwSZKkDgxhkiRJHRjCJEmSOjCESZIkdWAIkyRJ6sAQJkmS1IEhTJIkqQNDmCRJUgeGMEmSpA4MYZIkSR0YwiRJkjowhEmSJHVgCJMkSerAECZJktSBIUySJKkDQ5gkSVIHhjBJkqQODGGSJEkdGMIkSZI6MIRJkiR1YAiTJEnqwBAmSZLUgSFMkiSpA0OYJElSB4YwSZKkDgxhkiRJHYwthCV5f5Ibklw+bd39kpyV5Or273bj2r8kSdJCNs6esOOB/dZZdzjw+araFfh8uy1JkrTkjC2EVdWXgO+ts/oA4IS2fALwjHHtX5IkaSGb9Jiwn62q6wHav/efbcMkhyRZlWTV2rVrJ1agJEnSJCzYgflVdUxVrayqlcuXL+9djiRJ0kY16RD2nSQPAGj/3jDh/UuSJC0Ikw5hZwAHteWDgH+c8P4lSZIWhHFeouIU4DxgtyRrkrwIOBLYN8nVwL7ttiRJ0pKzbFxPXFXPn+Wuvce1T0mSpE3Fgh2YL0mStJgZwiRJkjowhEmSJHVgCJMkSerAECZJktSBIUySJKkDQ5gkSVIHhjBJkqQODGGSJEkdGMIkSZI6MIRJkiR1YAiTJEnqwBAmSZLUgSFMkiSpA0OYJElSB4YwSZKkDgxhkiRJHRjCJEmSOjCESZIkdWAIkyRJ6sAQJkmS1IEhTJIkqQNDmCRJUgeGMEmSpA4MYZIkSR0YwiRJkjowhEmSJHVgCJMkSerAECZJktSBIUySJKkDQ5gkSVIHhjBJkqQODGGSJEkddAlhSV6Z5Ioklyc5Jcm9etQhSZLUy8RDWJIdgZcDK6tqD2Az4HmTrkOSJKmnXqcjlwH3TrIM2BK4rlMdkiRJXUw8hFXVvwNHAd8CrgdurKoz190uySFJViVZtXbt2kmXKUmSNFY9TkduBxwA7ALsANwnyW+vu11VHVNVK6tq5fLlyyddpiRJ0lj1OB25D/DNqlpbVf8FnA78eoc6JEmSuukRwr4FPCrJlkkC7A1c2aEOSZKkbnqMCbsAOA24GLis1XDMpOuQJEnqaVmPnVbVm4A39di3JEnSQuAV8yVJkjoYKYQl2WPchUiSJC0lo/aEHZ3kwiR/mGTbsVYkSZK0BIwUwqrqMcALgJ2BVUn+Psm+Y61MkiRpERt5TFhVXQ28AXgt8Hjg3UmuSvKscRUnSZK0WI06JuyXkryD4XpeTwKeXlW/0JbfMcb6JEmSFqVRL1HxXuB9wJ9W1c1TK6vquiRvGEtlkiRJi9ioIewpwM1VdQdAknsA96qqH1fVSWOrTpIkaZEadUzY54B7T7u9ZVsnSZKkDTBqCLtXVf1w6kZb3nI8JUmSJC1+o4awHyV5xNSNJHsBN8+xvSRJkuYw6piww4BTk1zXbj8AeO54SpIkSVr8RgphVfXlJA8FdgMCXFVV/zXWyiRJkhaxUXvCAH4FWNEe8/AkVNWJY6lKkiRpkRsphCU5CXgIsBq4o60uwBAmSZK0AUbtCVsJ7F5VNc5iJEmSlopRvx15OfBz4yxEkiRpKRm1J2x74KtJLgRunVpZVfuPpSpJkqRFbtQQdsQ4i5AkSVpqRr1ExTlJHgTsWlWfS7IlsNl4S5MkSVq8RhoTluT3gdOAv2urdgQ+Nq6iJEmSFrtRB+a/DHg0cBNAVV0N3H9cRUmSJC12o4awW6vqtqkbSZYxXCdMkiRJG2DUEHZOkj8F7p1kX+BU4OPjK0uSJGlxGzWEHQ6sBS4D/gD4FPCGcRUlSZK02I367cg7gfe1H0mSJP2URp078pvMMAasqh680SuSJElaAtZn7sgp9wKeDdxv45cjSZK0NIw0Jqyq/mPaz79X1TuBJ425NkmSpEVr1NORj5h28x4MPWNbj6UiSZKkJWDU05F/M235duBa4DkbvRpJkqQlYtRvRz5x3IVIkiQtJaOejnzVXPdX1dvXZ6dJtgWOBfZg+NblC6vqvPV5DkmSpE3Z+nw78leAM9rtpwNfAr69gft9F/CZqjowyebAlhv4PJIkSZukUUPY9sAjquoHAEmOAE6tqhev7w6T3Bd4HHAwQJuT8ra5HiNJkrTYjDpt0QO5a1C6DVixgft8MMMUSB9I8pUkxya5zwY+lyRJ0iZp1BB2EnBhkiOSvAm4ADhxA/e5DHgE8P+q6uHAjxjmpryLJIckWZVk1dq1azdwV5IkSQvTqBdr/Uvg94D/BL4P/F5V/dUG7nMNsKaqLmi3T2MIZevu85iqWllVK5cvX76Bu5IkSVqYRu0Jg2Hw/E1V9S5gTZJdNmSHVfX/gW8n2a2t2hv46oY8lyRJ0qZq1EtUvInhG5K7AR8A7gl8EHj0Bu73j4CT2zcjv8HQyyZJkrRkjPrtyGcCDwcuBqiq65Js8LRFVbWau04KLkmStKSMejrytqoqhgur4rcZJUmSfjqjhrCPJPk7YNskvw98Dnjf+MqSJEla3EadO/KoJPsCNzGMC3tjVZ011sokSZIWsXlDWJLNgM9W1T6AwUuSJGkjmPd0ZFXdAfw4yTYTqEeSJGlJGPXbkbcAlyU5i+EK9wBU1cvHUpUkSdIiN2oI+2T7kSRJ0kYwZwhL8sCq+lZVnTCpgiRJkpaC+caEfWxqIck/jLkWSZKkJWO+EJZpyw8eZyGSJElLyXwhrGZZliRJ0k9hvoH5v5zkJoYesXu3Zdrtqqr7jrU6SZKkRWrOEFZVm02qEEmSpKVk1LkjJUmStBEZwiRJkjowhEmSJHVgCJMkSerAECZJktSBIUySJKkDQ5gkSVIHhjBJkqQODGGSJEkdGMIkSZI6MIRJkiR1YAiTJEnqwBAmSZLUgSFMkiSpA0OYJElSB4YwSZKkDgxhkiRJHRjCJEmSOjCESZIkdWAIkyRJ6qBbCEuyWZKvJPlErxokSZJ66dkT9grgyo77lyRJ6qZLCEuyE/BU4Nge+5ckSeqtV0/YO4HXAHfOtkGSQ5KsSrJq7dq1k6tMkiRpAiYewpI8Dbihqi6aa7uqOqaqVlbVyuXLl0+oOkmSpMno0RP2aGD/JNcCHwKelOSDHeqQJEnqZuIhrKpeV1U7VdUK4HnAF6rqtyddhyRJUk9eJ0ySJKmDZT13XlVfBL7YswZJkqQe7AmTJEnqwBAmSZLUgSFMkiSpA0OYJElSB4YwSZKkDgxhkiRJHRjCJEmSOjCESZIkdWAIkyRJ6sAQJkmS1IEhTJIkqQNDmCRJUgeGMEmSpA4MYZIkSR0YwiRJkjowhEmSJHVgCJMkSerAECZJktSBIUySJKkDQ5gkSVIHhjBJkqQODGGSJEkdGMIkSZI6MIRJkiR1YAiTJEnqwBAmSZLUgSFMkiSpA0OYJElSB4YwSZKkDgxhkiRJHRjCJEmSOjCESZIkdWAIkyRJ6mDiISzJzknOTnJlkiuSvGLSNUiSJPW2rMM+bwf+uKouTrI1cFGSs6rqqx1qkSRJ6mLiPWFVdX1VXdyWfwBcCew46TokSZJ66jomLMkK4OHABTPcd0iSVUlWrV27dtKlSZIkjVW3EJZkK+AfgMOq6qZ176+qY6pqZVWtXL58+eQLlCRJGqMuISzJPRkC2MlVdXqPGiRJknrq8e3IAMcBV1bV2ye9f0mSpIWgR0/Yo4HfAZ6UZHX7eUqHOiRJkrqZ+CUqquqfgEx6v5IkSQuJV8yXJEnqwBAmSZLUgSFMkiSpA0OYJElSB4YwSZKkDgxhkiRJHRjCJEmSOjCESZIkdWAIkyRJ6sAQJkmS1IEhTJIkqQNDmCRJUgeGMEmSpA4MYZIkSR0YwiRJkjowhEmSJHVgCJMkSerAECZJktSBIUySJKkDQ5gkSVIHhjBJkqQODGGSJEkdGMIkSZI6MIRJkiR1YAiTJEnqwBAmSZLUgSFMkiSpA0OYJElSB4YwSZKkDgxhkiRJHRjCJEmSOjCESZIkddAlhCXZL8nXklyT5PAeNUiSJPU08RCWZDPgb4EnA7sDz0+y+6TrkCRJ6qlHT9gjgWuq6htVdRvwIeCADnVIkiR10yOE7Qh8e9rtNW2dJEnSkrGswz4zw7q620bJIcAh7eYPk3xtrFUtHNsD3+1dRCe2fWmy7UuTbW/ylo6VTN5Sed0fNMpGPULYGmDnabd3Aq5bd6OqOgY4ZlJFLRRJVlXVyt519GDbbftSY9tt+1KzlNs+kx6nI78M7JpklySbA88DzuhQhyRJUjcT7wmrqtuTHAp8FtgMeH9VXTHpOiRJknrqcTqSqvoU8Kke+94ELLlTsNPY9qXJti9Ntn1pWsptv5tU3W1MvCRJksbMaYskSZI6MIRJkiR1YAjrJMn7k9yQ5PJ11v9Rm1fziiRv7VXfOM3U9iQfTrK6/VybZHXPGsdllrbvmeT81vZVSR7Zs8ZxmaXtv5zkvCSXJfl4kvv2rHFckuyc5OwkV7bf7Ve09fdLclaSq9u/2/WudWObo+3PbrfvTLIoL1kwR9vfluSqJJcm+WiSbXvXurHN0fY/b+1eneTMJDv0rrUnx4R1kuRxwA+BE6tqj7buicDrgadW1a1J7l9VN/Sscxxmavs69/8NcGNVvXnixY3ZLK/7mcA7qurTSZ4CvKaqntCxzLGYpe1fBl5dVeckeSGwS1X9Wc86xyHJA4AHVNXFSbYGLgKeARwMfK+qjkxyOLBdVb22Y6kb3RxtL+BO4O8Y3gOrOpY5FnO0fSfgC+1qAW8BWEKv+5qquqlt83Jg96p6ScdSu7InrJOq+hLwvXVWvxQ4sqpubdssugAGs7YdgCQBngOcMtGiJmSWthcw1QO0DTNcvHgxmKXtuwFfastnAb810aImpKqur6qL2/IPgCsZpms7ADihbXYCw4fUojJb26vqyqpa1DOhzNH2M6vq9rbZ+QyhbFGZo+03TdvsPswwY85SYghbWH4eeGySC5Kck+RXehfUwWOB71TV1b0LmaDDgLcl+TZwFPC6zvVM0uXA/m352dx1No1FKckK4OHABcDPVtX1MHxoAffvV9n4rdP2JWWOtr8Q+PSk65mkddue5C/b/3cvAN7Yr7L+DGELyzJgO+BRwJ8AH2k9Q0vJ81mkvWBzeCnwyqraGXglcFzneibphcDLklwEbA3c1rmesUqyFfAPwGHr9Agserb97m1P8nrgduDkXrWN20xtr6rXt//vTgYO7Vlfb4awhWUNcHoNLmQYL7F955omJsky4FnAh3vXMmEHAae35VOBRTkwfyZVdVVV/UZV7cUQvv+1d03jkuSeDB9GJ1fV1Ov9nTZ2ZmoMzaIcgjBL25eE2dqe5CDgacALapEOzh7hdf97FukQhFEZwhaWjwFPAkjy88DmLI3Z5qfsA1xVVWt6FzJh1wGPb8tPApbMqdgk92//3gN4A3B034rGo/VoHwdcWVVvn3bXGQwhnPbvP066tnGbo+2L3mxtT7If8Fpg/6r6ca/6xmmOtu86bbP9gasmXdtC4rcjO0lyCvAEhp6u7wBvAk4C3g/syXBa5tVV9YVeNY7LTG2vquOSHA+cX1WL8oMYZn3dvwa8i+F09C3AH1bVRb1qHJdZ2r4V8LK2yenA6xZjr0CSxwDnApcx9HAD/CnDGJmPAA8EvgU8u6pm/NLKpmqOtm8BvAdYDnwfWF1Vv9mlyDGZo+3vZmj/f7R15y+2bwjO0fYXMXwh507g34CXVNW/dylyATCESZIkdeDpSEmSpA4MYZIkSR0YwiRJkjowhEmSJHVgCNMmI8kdbdLXy5OcmmTLDXiOwzbwcW9Oss/6Pm6W5zo4yXun3f7d1qYrknw1yavnefwTkvz6xqhlY8rsk9KPNEl1ktcluSbDBPa/OW39fm3dNW1+xan1u7TZJa7OMAH85vPUt2ebm3N927VDktPW93HTHv+MJLtv6OPHoR2L89p77tIkz51237zHNYN3t9fk0iSPaOsflOSi9nt6RZKXtPVbJvlkhkmrr0hy5Ag1PiHJje25pn72afe9flrtq5P8alv/tCRfSXJJ+136gxH285kk30/yiTm22aIdi2vasVkx7b4Z37fSSKrKH382iR/gh9OWTwZetQHPcS2w/Xo+ZrMN2M+sj2GYtPm9bfnJwMXADu32vYDfn+e5j2C4fMlM9y3r+Po8DngEcPk6698KHN6WDwfeMsNjdwcuYfja/i4MF23drP38K/BghuvmXcIw4S8Ml3Z4Xls+GnjpPPX9z3Gf5HEDjgcOXEivF8MUabu25R2A64FtRz2uwFMYptoJwwwfF7T1mwNbtOWt2u/bDsCWwBOnbXMu8OR5anwC8IkZ1v8acN60/Wzf9nFPhmvu7dTWbwHsNsKx2Bt4+kz7mrbNHwJHt+XnAR+e633b4zX1Z9P8sSdMm6pzgf8FkORVrSfp8iSHtXX3aX95X9LWPzfJyxn+sz47ydltu99oPQIXt961rdr6a5O8Mck/Ac9OcnySA9t9e7e/ti9rvT9bzPSYEdvxOoZAdR1AVd1SVe+bbeP2F/hLgFe2HoDHttre3tr0liSPTPIvrcZ/SbJbe+xmSY5qdV+a5I/a+r0yzFV6UZLP5idXcH956024NMmH5mtIzT4x+yiTVB8AfKiqbq2qbwLXMMwc8Ejgmqr6RlXdBnwIOCBJGC5se9o8zzt13DYH3gw8tx235yY5IskxSc4ETkyyIsm57b1wcVpvY1t/eVs+OMnprffk6iRvneuYtOfYn2Fu0NVJHpLki0n+Ksk5wCuSPL31rnwlyeeS/Gx77FZJPjDt9fqttn629+yR016vo+aqq6q+Xm1+1vbeuwFYvh7H9QDgxBqcD2yb5AFVdVtV3dq22YJ2tqWqflxVZ7fl2xj+8NjQSasfAHx3aj9V9d3Whq0ZrrX3H239rTXCBOFV9XngB/NsNv09fBqwdztWs71vpZEs612AtL4yTG/0ZOAzSfYCfg/4VYa/yi9oH24PBq6rqqe2x2xTVTcmeRXDX+TfTbI9w1Xa96mqHyV5LfAqhg9rgFuq6jHt8fu1f+/F0LOxd1V9PcmJDHM/vnPdx4xoD2DkC7NW1bVJjmboFTyq1fQihp6NfarqjiT3BR5XVbdnOH3zVwxTgxzC8Nf6w9t998swrch7gAOqam2G01J/yTCn4+HALlV1a5Jt275WMlxc8cXr0ca7TFKddpX8dewInD/t9pq2DuDb66z/VeBngO9X1e0zbH83VXVbkjcCK6vq0NaWI4C9gMdU1c0ZTlPvW1W3ZLiq9ynAyhmebk+GyYhvBb6W5D1V9e0ZtqOq/iXJGQy9LKe1/cLQ6/T4dns74FFVVUleDLwG+GPgz4Abq+phU9vN9p7NcHr7mcBD2/NMvV77tzbPOklykkcy9E7963oc1x25++uyI3B9kp2BTzL8kfQnU39gTNvftgw9T++araZpHptk9bTbvwWcCbwxydeBzzH0Sp1TVd9rx/rfknwe+ARwSlXdOcpxmMf/tLf97tzIcKzmet9K8zKEaVNy72n/IZ/LMCXGS4GPVtWPAJKcDjwW+AxwVJK3MHwAnjvD8z2K4XTCP7cPxs0ZTnNMmWkOy92Ab1bV19vtExiu+P7OOR4zCadW1R1teRvghBYkiuE0DQzTQh099QHbPrT2YAiCZ7VjsBnDqSmAS4GTk3yMYUotqmoVsD4BbFQzTVRfzDxutebYfn2dUVU3t+V7Au9NsidwB0Owncnnq+pGgCRfBR7EXQPJKKa/T3YCPtx6IDcHvtnW78Nw6guAqvrPJE9j5vfsTQyzLRyb5JMMAYSqOoNhaqQZtX2eBBzUwsqox3XW7Vog/aUkOwAfS3JaVX2n7W8ZQ7h9d1V9Y7a6pjm3qp42Q917MfyeP5Hh2B1eVcdX1YuTPIzh2L0a2Bc4eL7jMILZ2rux3odaogxh2pTcXFV7Tl8xy4cGrZdqL4axK3+d5MyqevM6mwU4q6qeP8v+fjTDuhn3N89j5nIFQ2/MTzs91fT9/jlwdlU9M8Ppyy+29eHuHxABrqiqX5vhOZ/KMM5rf+DPkvzitB6S9fGddqrq+sw+SfUaYOdpt3diGN/DLOu/y3AKbFmrafr262P6cXslw3RKv8wQ/m6Z5TG3Tlu+gw37f3T6ft8DvL2qzkjyBIYxfzD76zXje7b1aO3NENwOpc1DO5vWY/pJ4A3tlCKMflzner2A4TRnkisYwtLU6c1jgKur6p38FNofHF8EvpjkMoZ5N49v910GXJbkJIZAe/BPs69mqr1rWpDchuHU+7zHQZqLY8K0qfsS8IwM3766D8MpmXPbX+E/rqoPAkcxDBiHYezH1m35fODRSabGlm2ZYeL0uVwFrJh6DPA7wDkzbZjk0CSHzvN8fw28NcnPtcdskWHs2lyPn96GmWwDTM3FdvC09WcCL2kfIiS5H8O8lcuT/Fpbd88kv5hhQu2d2zie1wDbMgy03hAzTlKdYezaidO2eV5r/y7ArsCFwJeBXTN8Y29zhoBxRlUVcDZw4AzP+8wkfz1DHaMct+ur6k6G13WzDWrthu136vU6aNr6MxnCFPA/py1nfM9mGBe2TVV9CjiM4ZTprNqx/CjDuK5Tp9avx3E9A/jdDB7FcNr0+iQ7Jbn3tHofzfAeI8lftLYetk4ts71es9W+W+46CfSeDKcgt2oh9i7rR33eeUx/Dx8IfKEdq9net9JIDGHapFXVxQx/AV/IMBnysVX1FeBhwIXt9OXrgb9oDzkG+HSSs6tqLUNIOSXJpQwfcA+dZ3+3MIxBO7X9BX4nwzfIZvJQfjJB72zP9yngb4HPtV6Di/hJz8psj/848My0gfkz3P9Wht6/f+auQeJYhkmiL01yCfC/2yDpAxkG9F8CrAZ+vT3ug62NXwHeUVXfT7IyybEztSXDBN3nAbslWZNhrBrAkcC+Sa5mOD00dXmCBwI3t+NwBcO38r7KcCr5ZVV1R+uNORT4LHAl8JG2LcDUeKhrGMbnHNfWP4Th9Ny6zgZ2b8ftuTPc/3+Bg5Kcz3Aqcr16NZMcm2HM3Lo+BPxJhoH3D5nh/iMY3k/nMvRETfkLYLsMXyy5hGEs42zv2a2BT7R15zD06pFk/yTr9gADPIehl/Pg/OTyD1PBbZTj+ingGwwD0d/H8O1BgF9gGJd5SavjqKq6LMlODL+HuwMXt/29eIbnXddjc9dLVBzI8MfACWlfQmjPeQRDL+FrMlwqYjXwf9qxmus40I77qQyD7dekXWYiw2Vp9m+bHQf8TDsmr2IYLznr+3aWtkh34wTe0phkuO7Qs1rQmfjjF7okbwNOqqpLN/LzfhB4ZQss2kjGdVx9vbSUGcIkSZI68HSkJElSB4YwSZKkDgxhkiRJHRjCJEmSOjCESZIkdWAIkyRJ6sAQJkmS1MF/A+ropUK9E5zEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "posterior_first = posterior.map(lambda v: v[0]) # extract var_0\n",
    "var_0_mean = posterior_first.mean\n",
    "posterior_first.plot_histogram(show=True, bins=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}