nb_pgm.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two general statistical models were applied to various datasets of planets. These models include:\n",
    "- 1 component model ($\\gamma$, $x_l$, $x_u$)\n",
    "- 2 component overlapping model ($f_1$, $f_2$, $\\gamma_1$, $\\gamma_2$, $x_{l,1}$, $x_{l,2}$, $x_u$)\n",
    "\n",
    "Made graphical below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import daft\n",
    "import numpy as np\n",
    "import pylab as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.10000000000000001, 0.40000000000000002)\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c3fa2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def powerlaw(xlist):\n",
    "    return xlist**(-1.1)\n",
    "\n",
    "xl = 2.5\n",
    "xu = 8.\n",
    "xs = np.linspace(xl,xu,100)\n",
    "\n",
    "plt.axes(aspect=8)\n",
    "plt.xlim(0., xu+2)\n",
    "plt.plot(xs, powerlaw(xs), linewidth=3, color='black')\n",
    "\n",
    "ylims = plt.ylim()\n",
    "plt.ylim(0.,ylims[1])\n",
    "plt.axvline(xl, 0., powerlaw(xl)/ylims[1], linewidth=3, color='black')\n",
    "plt.axvline(xu, 0., powerlaw(xu)/ylims[1], linewidth=3, color='black')\n",
    "\n",
    "plt.text(xl-1, 0.05, r\"$x_l$\", fontsize=18)\n",
    "plt.text(xu+0.5, 0.02, r\"$x_u$\", fontsize=18)\n",
    "plt.text(5, powerlaw(5)*1.2, r\"$\\gamma-1$\", fontsize=18)\n",
    "\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "plt.ylabel(r\"$p(x)$\", fontsize=20)\n",
    "plt.xlabel(r\"$x$\", fontsize=20)\n",
    "\n",
    "print(ylims)\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"figures/pgm_1comp_ex.eps\", dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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X13qWIJqbvLw8/Pz8iI+PZ9SoUXqXIyxgizvqjgXeAj4FPlFKNeiHKZqmdaOqE8Uk4Dml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\nJAkoIYQQhvT/AYIIx4EPdcROAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fbdea20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def powerlaw_1(xlist):\n",
    "    return 0.25*xlist**(-0.2)\n",
    "\n",
    "def powerlaw_2(xlist):\n",
    "    return xlist**(-1.1)\n",
    "\n",
    "xl1 = 1.\n",
    "xl2 = 2.\n",
    "xu = 8.\n",
    "xs_1 = np.linspace(xl1,xu,100)\n",
    "xs_2 = np.linspace(xl2,xu,100)\n",
    "\n",
    "plt.axes(aspect=8)\n",
    "plt.xlim(0., xu+2)\n",
    "plt.plot(xs_1, powerlaw_1(xs_1), linewidth=3, color='black')\n",
    "plt.plot(xs_2, powerlaw_2(xs_2), linewidth=3, color='black')\n",
    "\n",
    "ylims = plt.ylim()\n",
    "plt.ylim(0.,ylims[1])\n",
    "plt.axvline(xl1, 0., powerlaw_1(xl1)/ylims[1], linewidth=3, color='black')\n",
    "plt.axvline(xl2, 0., powerlaw_2(xl2)/ylims[1], linewidth=3, color='black')\n",
    "plt.axvline(xu, 0., powerlaw_1(xu)/ylims[1], linewidth=3, color='black')\n",
    "\n",
    "plt.text(xl1-0.75, 0.02, r\"$x_{l,1}$\", fontsize=18)\n",
    "plt.text(xl2+0.25, 0.02, r\"$x_{l,2}$\", fontsize=18)\n",
    "plt.text(xu+0.5, 0.02, r\"$x_u$\", fontsize=18)\n",
    "plt.text(6.0, powerlaw_1(6.0)*1.2, r\"$\\gamma_1-1$\", fontsize=18)\n",
    "plt.text(3.0, powerlaw_2(3.0)*1.2, r\"$\\gamma_2-1$\", fontsize=18)\n",
    "\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "plt.ylabel(r\"$p(x)$\", fontsize=20)\n",
    "plt.xlabel(r\"$x$\", fontsize=20)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"figures/pgm_2comp_overlap_ex.eps\", dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from matplotlib import rc\n",
    "rc(\"font\", family=\"serif\", size=12)\n",
    "rc(\"text\", usetex=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pmqRZkuann2d1WNfJqb5+sw+eLK5UzOx+PODlLWXX1Q8GVsSSpkp6r6R3p3C+urMD3kM2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\nGpoeDI4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d4922b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Instantiate the PGM.\n",
    "pgm = daft.PGM([4.0, 4.0])\n",
    "\n",
    "# Latent variables\n",
    "pgm.add_node(daft.Node(\"xn\", r\"$x_j$\", 2, 2))\n",
    "\n",
    "# Data.\n",
    "pgm.add_node(daft.Node(\"Rn\", r\"$R_j$\", 1, 2.75, fixed=True))\n",
    "pgm.add_node(daft.Node(\"pn\", r\"$P_j$\", 1, 2.00, fixed=True))\n",
    "pgm.add_node(daft.Node(\"Mn\", r\"$M_j$\", 1, 1.25, fixed=True))\n",
    "\n",
    "pgm.add_node(daft.Node(\"in\", r\"$i_j$\", 2, 2.75))\n",
    "\n",
    "# Hierarchical variables\n",
    "pgm.add_node(daft.Node(\"gamma\", r\"$\\gamma$\", 3, 3))\n",
    "pgm.add_node(daft.Node(\"xl\", r\"$x_l$\", 3, 2))\n",
    "pgm.add_node(daft.Node(\"xu\", r\"$x_u$\", 3, 1))\n",
    "\n",
    "\n",
    "# Add in the edges.\n",
    "\n",
    "pgm.add_edge(\"Rn\", \"xn\")\n",
    "pgm.add_edge(\"pn\", \"xn\")\n",
    "pgm.add_edge(\"Mn\", \"xn\")\n",
    "pgm.add_edge(\"in\", \"xn\")\n",
    "\n",
    "pgm.add_edge(\"gamma\", \"xn\")\n",
    "pgm.add_edge(\"xl\", \"xn\")\n",
    "pgm.add_edge(\"xu\", \"xn\")\n",
    "\n",
    "\n",
    "# And a plate.\n",
    "pgm.add_plate(daft.Plate([0.5, 0.75, 2, 2.625], label=r\"$j = 1, \\cdots, n$\",\n",
    "    shift=-0.1))\n",
    "\n",
    "pgm.render()\n",
    "pgm.figure.savefig(\"figures/pgm_1comp.eps\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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858UXX6xuS4grKysZP378divdlht1FRUVScd69tlnCYJgQyKR2G4jJYe8CXQSkT00g3SX\nLUglKjJvtdWasRh388+UdKM9B5ODUPEmTISjoyTd14qRMAwfXbRoUdZf9Pr6+qSBHXPnzk2o6qJs\nx0oHf3N8HEjdz64VxKUybTeVovdZPpEUPRgiZDGwt7hqI2mRynm1aD8At9EbmfmoRf8mwhFiQlw8\n/ODTTz8NXnghuzwxtbW1DBgwoM3PP/roI958880yVY0jjv8WYGo2fsqqOiWF8OExwPsx3Gw2AHfh\nNhzTPTaV82rOVGB2LgTSRDh6TIiLBFVtEJH5t956a8Zf+hkzZtDQ0LDFftwaN954YxgEwXv5FinP\nfJzN/mu5GsBvPF5C6qHUUTMLmCA5zPssInvhvCsi94s3Ec4NlvSniPAXwZtf//rXg1NPPTXy/l98\n8UV++MMfgvNfjSUvsYgcDvwOOMhvYEbd/3k4P9bhcYmIiFwL7K2+snjEfQtug+7vqnpFFv1sdx2a\nCOcOWxEXEar6NjDtt7/9rb711luR9r1+/XqmT58eishDcYkwgKo+jQvsmBl1KLWIfA6XfnJCzCJy\nOXCwiHw9B32fi3NbuzrKTk2Ec4utiIuQsrKyZ8rKyg6dMWNG0Lt37+QHJGH9+vVMmjQpsXbt2vfD\nMPxs3BeZiHQFngSeB74TRYIX7/r1N1wB0dQzIOUIEemP2ywcr9EV/DwJl5T9CM2y8kfz69BEOPfY\nirgICcNwRCKRWDJ16tRw0aLsTLlvvPEGZ511VmLt2rUfhmG4byFcZOoq8h6Dy23xSxHJKkxXRA7F\n5bC9qhBEGEBVa4ETgLtE5OwsM5MF4qqq3AB8OVsRbtG3iXAesBVxkSKO36nqKUOGDAmnTZsWpFPD\nLgxDbr/9dh599FGCIFgYhuEIVd2Ywymnjc8/exNwOC6SL62gGxHZEfgJziZ8rqo+HP0ss0NE+gH3\nAO8Ak7z5KZ3jq3CbcjsC31DV5RHNS3Fh9ybCecCEuMgRkSOCIPgD0H3AgAE6ceLE4LOfbTvT4Mcf\nf8ydd96pzzzzjDY2Nia8W9Sd+Ztx+ojIV3B13upw3g4Pa/ullP4L5yJ2Ni6H7fmq+n4+5poJ4kpE\nXYor//Mw7hwXtWWS8avnYTgXtWOA6cD1UQqlF+ImTIRzjAlxB0FEvhkEweVhGFaXlZWFu+yyS7jn\nnnuWd+7cmcbGRlatWpV477332Lx5c1kQBKvDMPw5cG2xXGBerE4AzsPluqjFBUi8jcsMVwH085/t\nCvwKmBVlPoxcIyK7AROAKbjzWYQLi/4IlyxoF1yI9GBc2taZwK9UNdJ8EmaOyD8mxB0MnyDoeGCM\niOwnIjuo6iZ11W4fB35fyKvDVBBXcmggTnRH40J/p+NyYSwCXilm8fAr3r1w53cw8ENgHXAdTpgX\nA+9EsYnZytgmwjFgQmwUNSLyXeDnHfk7480Ea1V1p6SNsxunuQjTkf9PCw3zmjAMo7XyRkYeMSE2\njBLHzBHxY0JsGCWMiXBhYEJsGCWKiXDhYEJsFC0i0htX0RkROSbm6eQEERnsf+3uw6Kj6tdEuIAw\nrwmjaBGRG3FJbspxhTn3SjcyrdARkXfZWuduuaruF0GfSUXYrsP8Yitio5hZCjSFZW/AhQl3NF7G\nXacBrpp3VthKuDAxITaKmcVsLRf/r1wEOBQAT+EiBzfgEhdljIlw4WL+gkYx8y+gC84skZVIFTAL\ngfX+94yLnZoIFza2IjaKFlXdjCsvnwAWxDydXLEYd7PZEWeKSRsT4cLHhNgodubjnuwyXi0WMqpa\nDzQA9arakOpxPk3qH0TkFUyEC56SME2ISA9c6ZhdcAli5gD3N5UEEpGJuIrut8c3y2jxeW6HAd2A\nT4F/AvM7ih3VFwGtAd7H2U93E5EPo85EFici0gXYH3gd+MS7r72cYt7o04CjcatpgF0KUYRFZFeg\nL27Fvxl4F6jrKN/TVCkJ9zURua+pUKOIzFTVc6PsvxAQkR2AH5WVlU1IJBKfAYLOnTsngiDQMAxl\n8+bNgapKEAQfh2H4MHChqn4Q87TTQkR2BsbjsssNBD4E3sNdxBuBzwGrgOeAXwJ/LbYL2tfVmwwc\nCeyLM71sxm1K7ghUAf/GlZKaraorWumjEngV6O7fSgBfVdU/pTGPnLiv+Rvol3B/x6G4xdErODt4\nOfBfuHm/CDwE/FpVP4l6HoVGhxfilqtdEXlcVb/Uos0iXJnzj4BRqjolqvFzjYh08jear+6www56\nxBFHlH3xi1+kX79+BMG2lqe6ujqeeuopnnjiicTatWvLgiB4IQzDYwpdkH2e3iuAk4E/4ipaLGw5\nbxEpw4nXUbicvuXAT4HfFbogi8gQ4CrgAFzFjT8A/1DVDS3adQX643IzT8CZZC5W1WX+cwHm4oRc\ncU9DZ6vqg2nOJ+rrUICzcAnw1+Cut7/hfKPDFm13Bz4PnIl7gr0HuExV10Q1n0KjFIT4QmCeqi71\nZWUubrkiFpHHVHW0//0q4F5VzWhjJJ+IyBgReaBLly47nn/++cHhhx+e8rEvvfQS1113XeKDDz5A\nVS9Q1Zk5nGrGiMiJwAzgXuBKVX0vxeMEOAJXamkFMMXbWwsK/yTzQ1w1kWnAb9qrPtLi2C44Mf4J\nrl7d1cBJOOHaiMs/fbaqrs5gXpFdh75iyu241e8FwIJUb4wisgeu6vUxuFJSc6OYU6FRCkLcA5iI\ne9Spbs0O3HyVLCJzVPWUqMbPFSJyEXDNsGHD9KKLLpLy8szM/XfddRcPPvigishvwzA8I9pZZo4X\n0qZV8DdVdX6G/ewAXIYTrDFNK8dCwCe4/yOwGpic6Y1CRPbCraJ3AAbhzBgTVPWhLOYWyXUoIkOB\nR3DVpa9R1cYM+zkaZ266RVWvynZehUaHF+IUxjsamATMBnriVs+fiMiAQl0VNyVDnzx5Mscee2zW\n/S1dupTLL79cgYIRY/9kMgoYncmKrpX+TsGtGo9S1X9l218E8+mOs/M+B3yn5eN5Bv2V4Z4ahgND\nVPU/SQ5J1l/W16HPk/En3E3hj9n05fvbA5iHsxtfmW1/hYQJsVtZLm7yoCh0ROTzwIJzzjlHjj/+\n+Mj6Xbp0KZdddpkC58VtphCRbwA/AA6L0n7t+/0xcLCqrouq3wzncj/wMe5xO5KL0Ivxb3HVPM7J\nsq+srkPvDfEPYKqqPpLNXFr0uwfOZfHbqvqHqPqNm5L2I/Y245Nxu+/N3z/ab/IVFCIiQRDMPfjg\ngzVVEZ4/fz51dXVJ2w0YMICxY8eKiNzkL6JY8BnVfg6cHvUmoqr+GhcyfHWU/aaLiJyMK3R6QZSb\niN49bSIwUkRGR9VvhtyAcxGNTIQBVPUd4JvATBHZJcq+46TkV8RtzKEKGJiNjS0XiMiMTp06Tbn3\n3nuDzp07J21fV1dHRUUFDQ0NVFRU0KtXr6THTJgwIfHhhx8uSiQSX4hizukiInOAV1X1shz13xOX\nPOdkVX0uF2MkGX8nnGvZ8ar6fI7GGImzGe+bos9xa31kfB36m8DNQH9VXZ+sfYZj3ADsqKqTctF/\nvjEhbn0OE4E5heS/6COlPj399NN3OPXUU3M2zksvvcS0adMAdsu3W5uI7I1zx9pbk0SR+ZvlbJzL\n4RxgV9xG1a2quiTJsecDI+LYlBWRqcCRqnpSjsd5Avilqv42w+OzEeK5OO+PX2dyfIpj7AosB/pG\nsYcQNyURWZcOzfyOC0aEPRNEpPO4ceOSNqyvr2fGjBl069aNESNGsHbtWpYvX86YMWPo06dPu8f2\n69eP7t27J9auXXstzu8zn0zGbcQkDeVV1ZXOsYLpqloLICIDgduAwe0dC/wa+KmI9FbVd7Occ8p4\nT5CpOBeuXDMDuAhnM84bItIXd0M8IZfjqOoHIvIw7jt6TS7HygclbSNuDVW9rTUXt7gRkfP79etH\nKm5qlZWVAJx88skMGzaM0aNHM2bMGG6++eaUxho1alRZEARfy2rCmXEScFca7Qc3ibCnD85nuF18\nYMAfgHyf4/64kPO/JWsoIgP9XsVV/t85aY71f8B+4hL+5JOxOD/8DUlbZs8vgYJ3NU2FkhViEakW\nkckiMt6HzhY0IrLvwIEDU35UXL58OVVVVVte19fXbxHoZIwYMYIwDHv4FVxe8H+DSlxOjFTaD2R7\n0Z0IXJLikAuAQ1KeYDQMJoVgBu/7vkJVnwSO9v9e0qLN0SKyT1t9eH/dhcRzjinZ3iO42SwC9ve+\n4kVNSQqxiAzHudZcj9tU+Jd3i4lzTuUicraPlvtMi8/KwjCsGDZsWEp9rVixYjvRfeyxxxg/fnxK\nx9fU1DQ9Rh/aYh47icgRIjLV+8FGySCgVlNPTDMSqBORo/xFfCJwkqq+7ufarlDhbNHbiJS3w+8p\nIseLyGk5uBEdQgpZ4lR1jfdlr8KJDU3n1azNky3fa4XFtDDTiEiZiPQTkTN9sEXUDCaFc0x2sxGR\nx5P14TcCVwAHZj7dwqBUbcS/Aiqavd4BmCEiOdmpT5EDgFuBdUAXEVmLyz/7FLASYM89U3vKrK2t\npbKyktpa99Te0NDAtGnT6Nq16zaft+dF0alTp8SmTZu+JiJfwIUKDwF2wyVn2RHYVUR+n8mJtsHn\ncVnGUmUUcFVb/t/+wm6PlcBeInK8H/tw4GCgM7AJ2AlYISJR7vrvB/w9WSMvUgDj8KImIgObNiHF\nBSGNUtVpSbpaCRwjImcCh/mfvrjzKwfe8eff1jwyEbg9SeHv2JQ3op2bTVITk2elH7Oo06CWqhD3\nbvG6HLe5kNMNhhTZyf+7Ky6N4dHpdrBkyRLGjRtH//6tF/1t6/3mBEEgwIX+pQJNq8MmkfiJ/4mS\ndBz0B7clwikKVZPYPtzKZ02pI3PhXpZKsMwknDfICmAXETkKL1aeRTiRTsZm4DjgxBbvN/k+VtN+\nHbxMw8E3J2uQ7GaDC3ZJdazkvpwFTqkK8b9xGayaTDMbcG5P345rQiKyP85c0ogTiX/gVsMLgTeB\nF8Mw3C6jWmssX768TbGtra1lyZIlSc0UiURCge/gyhENxq2KB+KEWHABFw+kcm6pICJn4BK7JGvX\nA/g+8IG0HYaeilDtiLvYh+LObyhuVXyA/7wL0E1VP03tDJIjLpquS7J2qnptks/XpGg16YJLAHQz\nzixyGC5H9T641JiLVXV4G3PNyH1NRDbinjCTbda1ebPxN9KFKQ7Zha0FZIuWUhXik3GPiF1xYvwv\nXHq+2FDVf3vb9X+Ad5pv6HhbpdbV1UlNTU2bfTQ0NHD//ffTvXt36urqqK6u3q5NTU0N8+e3nz8n\nDEM2b95cBjzu8zI8Dkz3c9kVJ1YZJeFphzpcCst28Y+00/xPm21SEKr9cCkY6/zY98GW/+sqYKco\nRdizwo+bFf5xPpVH9/2A11T1RVzSq9v88Z1xdtVV2c6lFer8uLXtNUpysxmFy5uRCvuRuhmjYClJ\nIVbV5SJSg1sVbwSWprFJlDPairRSVS0vL1/z3HPP9WxPiCsqKhg/fny7q92Kioo2P2ti2bJlAGFr\nyXF8kEdSO2cGLAUOEJHOmmIayLZIUaha3TjzN8DkMeGZsRiIIqnSSFzym2Qcgstgtw3+//fFCObR\nGov8uO0KcRJW48wm7SbdEhcl2QuXWL6oKUmvCQBVbVDVZ1V1cSGIcDLCMPzn4sWLs8rQBam5sT31\n1FOUlZW9n+1Y6eB3wF/FbZxlSypCNYLUH3+j4gXgUBHplGkHIjIL6NGGSaZ5u67AAHInuG3xAu7/\nNmNU9boU0wsMB14shus3GSUrxMWGqv50xYoVwfr12W3i19bWMmDAgHbbPP3004lEInFHVgNlxq9x\ntsOMSUWovKviF4EovT6SoqpvAC8DX82ijymqel0KTU8Dns53mDrOxHOCX63mmok4D6iix4S4SFDV\nx4MgWHP33Xdn3MeMGTNoaGho1XbcxNNPP83GjRuF6D0iUuEu4LiWftTpkKJQTcRFf8URxn4LcF4u\nB/B27vP8WHlFVVcBf8bVpMsZPi/JYcDvcjlOvrCkP0WEiFwoItfceeedsttuu0Xef2NjI6eddlq4\ncePGh8MwHBv5ACkgLqtWD1Udn6P+98GZJIarat5ti36j7J/AJaqakxW5iIwHvg0cohkmnM/mOhSR\nQTgxPtjuifo6AAAVaElEQVQLc6T4G81DwDJVvTzq/uPAhLjIKCsrW15ZWbnP7Nmzy6Lue/r06bpg\nwYL1qrqzqib1Bc0FItIN57p3gUZQ1aFF3wI8gavCElu5HRE5DLgfJ1SRZg7zuSWW4PyoM94wy/Y6\nFJErcV4w45KFdGfQ9+k4L6dDNMM0n4WGmSaKjDAMj3znnXe44YYbIv1yP/roozz33HOiqifGJcIA\n6ipnnA3cLq60fJT8FBdRmYqNNWeoq7/3G+BecQVAI8HfxB4AbspGhCPixzgh/l6UnfocI/8LjO8o\nIgwmxEWHqr4FHDtv3rzIxPiRRx7h1ltvBbhIVZPG+OcaVf0rLmjjCRE5IFn7ZPgcEj/GZQb7qmZY\nwDJipuEqw/zeezhkhbiE838DakgvQjEn+OxrXwbOE5FIxFhEDsHVwDtXVRcla19MmBAXIepKih8z\nb968cPLkyYnVqzN7ut2wYQOXXnpp4vbbb1fguynuxucFVb0LJ8ZPicjETBPwiCu99DBwLHCEqubV\nLa8tvMvV6bigioUiMiTTvkRkBM5HeSEu5PdFEflZNm5yUaCugOnhwFki8jsRyWhjQ0QCEfk28BhO\nhB+Mcp6FgNmIixgR2SsIgr+oap/Ro0fLhAkTtiT2aY/Gxkbuv/9+7r///jCRSKwJw3CMqr6Qhymn\njU88cxdu9fhj4NlUbI5+hXgmcBkuouynhfgo628wp+Iet+8BblDVN1M8tg/wXVxe5amq+rCIHA78\nFRcm/xauJFTa1cijvA79iv9nOJe6H+KqdyRN/u//b76I+7sHuGrQr0Uxp0LDhLgDICIXBkHwgzAM\ne1ZXV4eDBg0KDj30UGpqarbkpnj77beZP38+S5cu1ZdeeglV3aQuAX6kBSxzgV/ZTcFVtvgUJ1gv\nAEuaXND8RVuNi+o6ChfG/iRwpQ/xLWhEpBL3BHAGLnLxUVyU2r+abPbNQpMH4xJUDcHdpK5q7i/s\nfam/ydacD9cDP0knYjEX16GIHIozyRyGqxzyFG4l/0bTd9D7Hw/CBfacCYS4QqR3doTAjbYwIe5A\niMhIEbksCIKDE4lEU3KeLQRBsE5VX1PVG/2jf1EhIgEuG93xOME9GHehBv5nNe7CXgD8Sl3F36JC\nRCpwK+Qv4gS3Cpd6VHCJipbjzvFJXJXk7fJh+D5eY2uWwRA4UdOoqJzL69D7AH8Dl2jpEKAn7gZb\njvs71uLO8UHg74W+UIgCE+IOil8hVgLdgQagvqOtKESkDPhvXEKiz8QUoJFTxFWfqMClIm1IdVXr\nTRRzceIN0EtV30tj3Lxdh97bowvOvr2uo31PU8GE2ChqROReXN2yg1Q1pTJLpYKIXAHsDXzdv5Vy\nZW67DvOLCbFR1IhIU4WGiaqaefx3B8bblps2KlMSY7sO84u5rxlFi4jsCHwW6IRLeG60gjdnNBXY\nXO1zShsFhAmxUcz0x21kgUuJaLSBiXFhY0JsFDOH4FbDADUiUpKFDlLFxLhwMSE2ipkqtnoFBEDG\n6TNLBRPjwsSE2ChmLmdrzt3Pqeq7cU6mWDAxLjxMiI2iRV15pRX+96IvIJlPTIwLCxNiwyhRTIwL\nBxNiwyhhTIwLAxNiwyhxTIzjp8MLsYj0EJFZInKfiHwoIjNF5KhW2k0UkXPimKNhxE1LMY5zLqVI\nhw9xFpH7VPVk//tMVT03qr4LERH5MnBCEATDRGQPVS0XkYSqfhCG4fO4oo73FmtiFR+uOwTnQ9yU\ngW0ALm3kK7jUkQvUla430iSTcGgjezq0EIvIREB93l1E5HFV/VKLNvfhhOkh/7oHLsXgOFV9PYp5\n5BoR2Rm4zhdV3GHnnXdOVFdXl/Xp00d22GEHNm3axH/+8x9ee+21xtWrVwdhGCrwZ1X9tqrWxTz9\nlBCRzwKTgInAO7h8xIuBt4EE0BXohxPn4cAynGvbIwVSGqloMDHOPx09EqkHMA9ARKrwrk4tmINb\nYT3kX1cDTxSRCF8IXN29e3c97rjjyk466STKy8vb+ruWh2HIvHnzmDNnzpj33ntvuYjcAUwq1Jyv\nPlrue8BFwO+Ao1X1X200f9gf0xk4EVe94jIRGZ9JlYpSRVU3NatMtVpETIxzTEdfEffAraBeBKqb\nVsYt2gzECdG5XqwH4VbRD7VsW0iIyI5BECxW1c+dfvrpcuqpp6bdx9NPP80vfvGLMAzDj8IwPKTQ\nHud9AvH7gHXA2eneHH1O5jOBa3GliK4s1BtOoSEiirMZ28o4D3RoIU5hrAGqulREZqnqFC/c3wem\nNyvBM6DQVlMiUhEEwesVFRU733DDDWWf+Uzmkb3r16/noosuSrz11lsJVT1IVV+NcKoZIyI1wF+A\nG4GfZyOgIrIn8AiuckfBl4YqBJquQzNT5IcO7zWRhC1uOl5w1+BWzlsqPRSgCEsQBK9079595zvv\nvDMrEQbo2rUrN910U1lNTU2ZiNR6e3OsiEgv4AngZ6p6XbbCqapv4+rYDQF+GsEUSwZzbcsPJSvE\n3gwxyVf7XQ7UicjRQJV/DxE52m/4FRK3BUHQe9asWWVdunSJpMMgCLjuuuvKevbs2SkIgnmRdJoh\n3pwwC5ijqrdG1a+/uX4FmCAiR0TVbylgYpx7SlaIVXWlqp6iqp/4Vdcnqvqkqg5ptiKuAwrmUUxE\nDgHO+t73vhd069Ytafv58+dTV5eaU0QQBFxxxRVlqjoo5pvPqUBfXNn1SFHV1bhq0Hf4AptGipgY\n55aSFeIUGYn3uigEgiD49b777qvDhyfPgb5ixQpqamoAWLVqVUr977XXXowePZogCK7PaqIZ4ouB\nXoUre7SxjTZVPkDn8TY++7C9wBxVfRRYghNkIw1MjHOHCXEbNPNBLojKwCLSOwzD/c8999yU/mZ9\n+vShV69eVFdX06tXr5THOfvss1HVChH5asaTzZyvAO+o6nNtNVDVlcD9uFzELRkELGzNO6YF1wNT\nRMS+/2liYpwb7IvYBqp6WwoXdD65pmfPnommVW5r1NfXM2PGDC677LJWPzvttNN47LHH2h2kS5cu\nHHDAARoEwRVZzzh9JrM1v3AyPm7+wrsh7oIT6WQswLnEbRfqbiTHxDh6TIiLhLKysiOHDBlS1l6b\nyspKhg8f3qopYsWKFfTt25fRo0cnHWvkyJGBqu6b+WzTx69ORwB/TNKuChfGXCci+zR7rw4YRQqm\nJO+F8Ufg8KwmXcKYGEdLSQqxiHQWkVtE5AMReVdEzot7TskIw7By8ODBKbWtqNh2H2rFihWsW7eO\nww47LKXjhw0bhqp2zrMr277AalX9MEm7Ku9muBIXBQnQw783qHnQh/d62aeNfhYBqf2HGq1iYhwd\nJSnEwAxgPO5RthK4RkS+EeeERGQPf1P4h79JnCEi+4tImYj0UNWyZEJcX19PTU0NlZWVW1bF9fX1\nVFZWsmTJEgYMGJDSXLp27UpZWVkIfFkc+4jIOBG5VkSe9xtiQ7M95xYcBNSm0X4F0KdZUE4VLvfE\nFrwXzOttHF/rxzSywMQ4Gjp6rom2OJWtRSfBJYyZLSK/imk+zanECcQ3cDfKctzqj86dO7d74KpV\nq6isrKRXr17U19fTq1cv1q9fT2VlJXV1ddts2tXW1m5p2xrl5eWaSCSmA7cCZcAmoJufkwILmuUj\niIpU7LtNg9bhkgA94V+PbPY73id8lKpOa6Ofj4GdMpyn0Qyfm6IpHDql3BQi0gk4AJekqS/uetwM\nvIu7oS4plI3yfFCqQtxaNq5PgPp8T6QZe7B1ZbEBCIEuuExjdcB+qXbUu3dv6uvr6d69O9XV1dTX\n19OnT59t2vTv3z+Vrt7FXVxVOAH8FKjwcyvD3yAiohtO4FvFh59f7ds8iTMtDFTV173oXgw80OyQ\nRcC4dsYT3HkYEZCqGIvIwcC5wGlsFd2XgfeATjhz00nAQSLyLG7z9v86ega9UhXi/8VduF396/XA\nmaq6nW9qvvCPdH8C3gSexn1Ba1W1wQcfrFu/fj1du3ZtrxvAbdrNnTt3iymitrZ2G7NEbW0tS5Ys\nYfz48W320djYKMB1qvqgzzfQPMXkAOAMVf1nRifbCiLyNeDstj73NuApLV5f539/Ereq2qZ9khX7\nbrTwvDCyoz0xFpE9gJk4u/xs4ABVfaetvnw/43DX6c9FZKKq/iXnJxETpSrEPwHW4DJzbcDlNIhN\nhAH8F7ZVu6uqNgRBsPn555/vdOSRR273eUNDA3fddRciQv/+/ampqaFv37706tWL2tpaHnzwwW02\n6mpqapg/f36bc/n4449JJBIBMNePvwkXBLEEyJVL31JgYFSdtZP2tImBfkwjQloTY2AM8AucEJ/k\nv0/J+tkI/Ab4jYgcA9wtIo8C31XVDbk7g3go6exrxUR5efnK4cOH73PhhRdG0t8tt9zC1KlTW/3s\nT3/6E7Nnz96QSCR2bLVBDvA5JlYD/VQ1axORD8hZ2FbSJhG5BvhEVX+W7VgdkWyvwxZZ21YCY1V1\nSRb99cQtAnYFjlPVdZn2VYiUqtdE0ZFIJP64aNGiSMobNXlStMXcuXMTqpqOB0PWeN/eecDYbPsS\nkVk4l7a2RDjAJY4vmPD1joZf9X4Xt+8yPBsR9v19DJyCE/WHvdB3GEyIi4fvNzQ0BEuWZPV9Bra3\nGTdnzZo1rFy5skxVv5v1QOkzE5gqWbpjqOoUVb2unSajcJuzz2czjtE2PkHVNOAL7dmC00FdncWJ\nOA+e/4miz0LBhLhIUNW1IrJw1qxZWa2KZ8yYQUNDA9XV1a1+fvPNN2sQBKtV9dlsxsmQp/y/X8nV\nAF7kLwZusQTxucHbiO/C2XMjrfrixfgcXK6QQVH2HSdmIy4ixJUOqpswYUJw4oknRt7/smXLuPTS\nSwGOUdU/Rz5ACojISOBO4CDvGRF1/+fgvC++0NFdorIhm+tQRL4FjAaOzdXNTkQmABNUtUOEqZsQ\nFxkicrmI/Gj27NnSu3fvyPrdsGEDZ555Zrhhw4bHwjA8JrKOM8DbeLsC34zyQhaRPriEP0ep6rKo\n+u2IZHod+ieOl3E1Bp+JfmZbxukEvA6M6Qh/SzNNFBmq+hMRWXLBBReE77//fiR9btq0iSlTpiQ2\nbtz4oaoeH0mn2XERzm95erb24iZE5LPA48D/dIQLt4A5Cuct0bZ/ZASo6mZc1Oe5uRwnX5gQFyFh\nGA7evHnzy5MnTw6XLctOU+rr6znrrLMSH3300SdhGO7rv+Cxoqprcb6nY4AZIpKVG51Pkfl3YIaq\nzo5gikbbfAl4IE/29/txJpCix4S4CFFVDcPwwMbGxj9deumlXHPNNdrYmL6585577mHSpEm6du3a\nf4dhuJeqfpSD6WaEqr4PHImLgFsiIl9Itw+fZe/HwGPApaoaS+WREuMQXHh5u4jIQJ8d7yr/75wM\nxnoF2D3PWQJzgtmIixwR+YqI3BcEQZehQ4fKOeecI+1Vdl6/fj133303Tz75ZGLTpk2o6ndV9cY8\nTjltROQk4EZcZN8twJ/97nlb7XvhdtYn47KsTY7KhapUyMJGvBo4sL2gHJ83RFX1ExFZqKpDRGSf\ndjLltTfeMzhz09/SPbaQMCHuAHg76nlBEHw/DMM9OnXqlNh9993Za6+9yjp37kxjYyPvvvtu4t13\n32XDhg1lQRCsCcNwJvAjbaM2XKHhzRMnA+cBfXC5OBYDb+OSOFWwNR/GPsAcYGa2gQSlSibXof8e\nJoBO7d0om7WvAi5W1YztvCLyMHC3qv4+0z4KARPiDoZfDZ4IjAyCYF9cRrdNYRi+BfwNeFBVl8c4\nxawRkd44wR0E7I7L2rUe96i6GFjWEfMR5JMshbhcVdvMbOdXxODSmH6kqreLyEBVXeLt+ZNVdYqI\nXATMbi8dpog8BPxGVR9MZ66FRqkm/emwqOoqXITazLjnkitU9V3g//yPUSCoqopIAy7Pc3uZ7SYB\nH+GSMu0iIkex1a5cx9Z0qH3aE2HPTrj6g0WNCbFhGFHyT6A/W6Mkt0NVr23ns23Sl4rITm2JsV+B\n9/djFjXmNWEYRpQsxpmNsmGFiIzFrYxbj8V3/BfOFFL0G7FmIzYMYzuy8Jo4GZikqiNzMK2WY03B\nRUmenOuxco2tiA3DiJJHcGWOUi7tlQneLDEVV+2j6DEhNgwjMrw75B3Af+d4qCNxHkEdonxSUQqx\niFSJSDSlKtgS5TMxqv4Mo8S5HjhBRIblonMR6QrMAqZ1lFSmRSnEqroySeLvlPEVgL8P9EjW1jCM\n5KjqauB84Je+8G3UXAEsKvYgjuYUpRBHiboKwE/EPQ/D6Ej4AIu/Aw/4RPGRICLnAccBF0TVZyFQ\nVEIsIj2aJQrZKe75ZIs3sUz0PwPMRGJ0MKYAa4H/yzYxj4gEInIJLkXqKHVVzzsMRSXEQJVfwVYD\nu7T80Av1RBE5p42ffbIZXESWt9ZHa++31bYFioskGuQLXdYBOXf7MYx84CugnA68BCwTkYxKYPnr\n6Alc6P4IVV0Z1RwLhaL0I27K2BThmBNxVX/btTu3FeXT2vvtRQS1aHcVcK+qLvVO7FVR2b8NI1Oi\n9ucXkSNx3hT/Bm4GHmsvH4U/Zj9c4vczgGuA6ztqeauiC3H2GZtazXfqk4mcjFtptvwSKTAvk1R7\nWzpoQ1hbez8VEfaMVNVp/vdTgHOaEqBkOE3DKDhU9a8iciBwGm6zbaaIPI2LxPsXLmlTJ1y03CHA\n53FPvncAh0RdhLTQKDohBsbRxuaaLzZ5Wzqdea+JUUAPEXlRVf/i318EnONNBpHQRp8rWvw+mBQS\naxtGsaGq64E7RORO4EBgKE50vwrsCGwG3sWJ8yPA/GJJ05otRWOaEJEqVV0pIo+pal7Ko4jIgCiF\nOFd9GkbUWKqB/FJMQnwfcC/wcdOqNcfziNw8YCYHo1gwIc4vRSPEhmHkD7sO80uxua8ZhmF0OEyI\nDcMwYqYQvSbeEJHCspcYRunRod3FCo2CsxEbhmGUGmaaMAzDiBkTYsMwjJgxITYMw4gZE2LDMIyY\nMSE2DMOIGRNiwzCMmDEhNgzDiBkTYsMwjJgxITYMw4gZE2LDMIyYMSE2DMOIGRNiwzCMmDEhNgzD\niBkTYsMwjJgxITYMw4gZE2LDMIyYMSE2DMOIGRNiwzCMmDEhNgzDiBkTYsMwjJgxITYMw4gZE2LD\nMIyYMSE2DMOIGRNiwzCMmDEhNgzDiBkTYsMwjJgxITYMw4gZE2LDMIyYMSE2DMOIGRNiwzCMmDEh\nNgzDiBkTYsMwjJgxITYMw4gZE2LDMIyYMSE2DMOIGRNiwzCMmDEhNgzDiBkTYsMwjJgxITYMw4gZ\nE2LDMIyYMSE2DMOIGRNiwzCMmPl/Cq1NlyAElLwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11094a0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Instantiate the PGM.\n",
    "pgm = daft.PGM([6.0, 4.0])\n",
    "\n",
    "# Latent variables\n",
    "pgm.add_node(daft.Node(\"in\", r\"$i_j$\", 4, 2.75))\n",
    "pgm.add_node(daft.Node(\"xn\", r\"$x_j$\", 4, 2.00))\n",
    "\n",
    "pgm.add_node(daft.Node(\"Rn\", r\"$R_j$\", 3, 2.75))\n",
    "pgm.add_node(daft.Node(\"pn\", r\"$P_j$\", 3, 2.00))\n",
    "pgm.add_node(daft.Node(\"Mn\", r\"$M_j$\", 3, 1.25))\n",
    "\n",
    "# Hierarchical variables\n",
    "pgm.add_node(daft.Node(\"gamma\", r\"$\\gamma$\", 5, 3))\n",
    "pgm.add_node(daft.Node(\"xl\", r\"$x_l$\", 5, 2))\n",
    "pgm.add_node(daft.Node(\"xu\", r\"$x_u$\", 5, 1))\n",
    "\n",
    "# Data\n",
    "pgm.add_node(daft.Node(\"Rnhat\", r\"$\\hat{R}_j$\", 2, 2.75, observed=True))\n",
    "pgm.add_node(daft.Node(\"pnhat\", r\"$\\hat{P}_j$\", 2, 2.00, observed=True))\n",
    "pgm.add_node(daft.Node(\"Mnhat\", r\"$\\hat{M}_j$\", 2, 1.25, observed=True))\n",
    "\n",
    "pgm.add_node(daft.Node(\"sigmaRn\", r\"$\\sigma_{\\hat{R}_j}$\", 1, 2.75, fixed=True))\n",
    "pgm.add_node(daft.Node(\"sigmapn\", r\"$\\sigma_{\\hat{P}_j}$\", 1, 2.00, fixed=True))\n",
    "pgm.add_node(daft.Node(\"sigmaMn\", r\"$\\sigma_{\\hat{M}_j}$\", 1, 1.25, fixed=True))\n",
    "\n",
    "\n",
    "# Add in the edges.\n",
    "pgm.add_edge(\"Rn\", \"pn\")\n",
    "pgm.add_edge(\"xn\", \"pn\")\n",
    "pgm.add_edge(\"Mn\", \"pn\")\n",
    "pgm.add_edge(\"in\", \"xn\")\n",
    "\n",
    "pgm.add_edge(\"Rn\", \"Rnhat\")\n",
    "pgm.add_edge(\"pn\", \"pnhat\")\n",
    "pgm.add_edge(\"Mn\", \"Mnhat\")\n",
    "\n",
    "pgm.add_edge(\"sigmaRn\", \"Rnhat\")\n",
    "pgm.add_edge(\"sigmapn\", \"pnhat\")\n",
    "pgm.add_edge(\"sigmaMn\", \"Mnhat\")\n",
    "\n",
    "pgm.add_edge(\"gamma\", \"xn\")\n",
    "pgm.add_edge(\"xl\", \"xn\")\n",
    "pgm.add_edge(\"xu\", \"xn\")\n",
    "\n",
    "\n",
    "# And a plate.\n",
    "pgm.add_plate(daft.Plate([0.5, 0.75, 4, 2.625], label=r\"$j = 1, \\cdots, n$\",\n",
    "    shift=-0.1))\n",
    "\n",
    "# Render and save.\n",
    "\n",
    "pgm.render()\n",
    "pgm.figure.savefig(\"figures/pgm_1comp_sigmas.eps\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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f0K8RxmUZ7hvwS0lPFpfj/jCUzWlG9w76S99zEXRFnn5yGuuYa2aX4sHH/wN4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fad3668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Instantiate the PGM.\n",
    "pgm = daft.PGM([4.0, 4.0])\n",
    "\n",
    "# Latent variables\n",
    "pgm.add_node(daft.Node(\"xn\", r\"$x_j$\", 2, 2))\n",
    "\n",
    "# Data.\n",
    "pgm.add_node(daft.Node(\"Rn\", r\"$R_j$\", 1, 2.75, fixed=True))\n",
    "pgm.add_node(daft.Node(\"pn\", r\"$P_j$\", 1, 2.00, fixed=True))\n",
    "pgm.add_node(daft.Node(\"Mn\", r\"$M_j$\", 1, 1.25, fixed=True))\n",
    "\n",
    "pgm.add_node(daft.Node(\"in\", r\"$i_j$\", 2, 2.75))\n",
    "\n",
    "# Hierarchical variables\n",
    "pgm.add_node(daft.Node(\"f\", r\"$f_k$\", 3.25, 3.0))\n",
    "pgm.add_node(daft.Node(\"gamma\", r\"$\\gamma_k$\", 3.25, 2.5))\n",
    "pgm.add_node(daft.Node(\"xl\", r\"$x_{1,k}$\", 3.25, 2.0))\n",
    "pgm.add_node(daft.Node(\"xu\", r\"$x_u$\", 3.25, 1.0))\n",
    "\n",
    "\n",
    "# Add in the edges.\n",
    "pgm.add_edge(\"Rn\", \"xn\")\n",
    "pgm.add_edge(\"pn\", \"xn\")\n",
    "pgm.add_edge(\"Mn\", \"xn\")\n",
    "pgm.add_edge(\"in\", \"xn\")\n",
    "\n",
    "pgm.add_edge(\"f\", \"xn\")\n",
    "pgm.add_edge(\"gamma\", \"xn\")\n",
    "pgm.add_edge(\"xl\", \"xn\")\n",
    "pgm.add_edge(\"xu\", \"xn\")\n",
    "\n",
    "# And a plate.\n",
    "pgm.add_plate(daft.Plate([0.5, 0.75, 2, 2.625], label=r\"$j = 1, \\cdots, n$\",\n",
    "    shift=-0.1))\n",
    "\n",
    "pgm.add_plate(daft.Plate([2.75, 1.5, 1.0, 1.875], label=r\"$k = 1, 2$\", \n",
    "    label_offset=[17.,3.], shift=-0.1))\n",
    "# Render and save.\n",
    "\n",
    "pgm.render()\n",
    "pgm.figure.savefig(\"figures/pgm_2comp_overlap.eps\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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uNDQ00L17d/r27Zt3nwkTJjS+//77CxobG7+UxJgLRUTmAP9S1QvK1H5vLHnO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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110e3b390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Instantiate the PGM.\n",
    "pgm = daft.PGM([6.0, 4.0])\n",
    "\n",
    "# Latent variables\n",
    "pgm.add_node(daft.Node(\"in\", r\"$i_j$\", 4, 2.75))\n",
    "pgm.add_node(daft.Node(\"xn\", r\"$x_j$\", 4, 2.00))\n",
    "\n",
    "pgm.add_node(daft.Node(\"Rn\", r\"$R_j$\", 3, 2.75))\n",
    "pgm.add_node(daft.Node(\"pn\", r\"$P_j$\", 3, 2.00))\n",
    "pgm.add_node(daft.Node(\"Mn\", r\"$M_j$\", 3, 1.25))\n",
    "\n",
    "# Hierarchical variables\n",
    "pgm.add_node(daft.Node(\"f\", r\"$f_k$\", 5.25, 3.0))\n",
    "pgm.add_node(daft.Node(\"gamma\", r\"$\\gamma_k$\", 5.25, 2.5))\n",
    "pgm.add_node(daft.Node(\"xl\", r\"$x_{1,k}$\", 5.25, 2.0))\n",
    "pgm.add_node(daft.Node(\"xu\", r\"$x_u$\", 5.25, 1.0))\n",
    "\n",
    "# Data\n",
    "pgm.add_node(daft.Node(\"Rnhat\", r\"$\\hat{R}_j$\", 2, 2.75, observed=True))\n",
    "pgm.add_node(daft.Node(\"pnhat\", r\"$\\hat{P}_j$\", 2, 2.00, observed=True))\n",
    "pgm.add_node(daft.Node(\"Mnhat\", r\"$\\hat{M}_j$\", 2, 1.25, observed=True))\n",
    "\n",
    "pgm.add_node(daft.Node(\"sigmaRn\", r\"$\\sigma_{\\hat{R}_j}$\", 1, 2.75, fixed=True))\n",
    "pgm.add_node(daft.Node(\"sigmapn\", r\"$\\sigma_{\\hat{P}_j}$\", 1, 2.00, fixed=True))\n",
    "pgm.add_node(daft.Node(\"sigmaMn\", r\"$\\sigma_{\\hat{M}_j}$\", 1, 1.25, fixed=True))\n",
    "\n",
    "\n",
    "# Add in the edges.\n",
    "pgm.add_edge(\"Rn\", \"pn\")\n",
    "pgm.add_edge(\"xn\", \"pn\")\n",
    "pgm.add_edge(\"Mn\", \"pn\")\n",
    "pgm.add_edge(\"in\", \"xn\")\n",
    "\n",
    "pgm.add_edge(\"Rn\", \"Rnhat\")\n",
    "pgm.add_edge(\"pn\", \"pnhat\")\n",
    "pgm.add_edge(\"Mn\", \"Mnhat\")\n",
    "\n",
    "pgm.add_edge(\"sigmaRn\", \"Rnhat\")\n",
    "pgm.add_edge(\"sigmapn\", \"pnhat\")\n",
    "pgm.add_edge(\"sigmaMn\", \"Mnhat\")\n",
    "\n",
    "pgm.add_edge(\"f\", \"xn\")\n",
    "pgm.add_edge(\"gamma\", \"xn\")\n",
    "pgm.add_edge(\"xl\", \"xn\")\n",
    "pgm.add_edge(\"xu\", \"xn\")\n",
    "\n",
    "\n",
    "# And a plate.\n",
    "pgm.add_plate(daft.Plate([0.5, 0.75, 4, 2.625], label=r\"$j = 1, \\cdots, n$\",\n",
    "    shift=-0.1))\n",
    "\n",
    "pgm.add_plate(daft.Plate([4.75, 1.5, 1.0, 1.875], label=r\"$k = 1, 2$\", \n",
    "    label_offset=[17.,3.], shift=-0.1))\n",
    "# Render and save.\n",
    "\n",
    "pgm.render()\n",
    "pgm.figure.savefig(\"figures/pgm_2comp_overlap_sigmas.eps\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}