bearloga/pavement.ipynb

## pavement.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's an example of a [Bayesian network](https://en.wikipedia.org/wiki/Bayesian_network) (BN) using [PPL](https://en.wikipedia.org/wiki/Probabilistic_programming_language) in Python called [pomegranate](https://pomegranate.readthedocs.io/en/latest/)\n",
    "\n",
    "There are multiple ways to create a BN. You could specify the structure & probabilities, you could specify structure & learn probabilities from data, or you could learn both structure *and* probabilities from data. This is an example where the structure & probabilities are provided by us."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pomegranate import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose it rains 25% of the time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "raining = DiscreteDistribution({'Yes': 0.25, 'No': 0.75})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and that the sprinkler has a probability of 0.1% of being on when it's raining and a probability of 80% of being on when it's not:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "sprinkler = ConditionalProbabilityTable(\n",
    "    [['Yes', 'On', 0.001],\n",
    "     ['Yes', 'Off', 0.999],\n",
    "     ['No', 'On', 0.8],\n",
    "     ['No', 'Off', 0.2]],\n",
    "    [raining]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "now, let's describe the conditional probabilities of the pavement being wet/dry given the weather and the state of the sprinkler:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "pavement = ConditionalProbabilityTable(\n",
    "    [['Yes', 'On', 'Wet', 1.0],\n",
    "     ['Yes', 'On', 'Dry', 0.0],\n",
    "     ['Yes', 'Off', 'Wet', 1.0],\n",
    "     ['Yes', 'Off', 'Dry', 0.0],\n",
    "     ['No', 'On', 'Wet', 0.75],\n",
    "     ['No', 'On', 'Dry', 0.25],\n",
    "     ['No', 'Off', 'Wet', 0.01],\n",
    "     ['No', 'Off', 'Dry', 0.99]],\n",
    "    [raining, sprinkler]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "then we specify these as nodes in the network and specify the relationships between them as edges:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "s1 = Node(raining, name = 'raining')\n",
    "s2 = Node(sprinkler, name = 'sprinkler')\n",
    "s3 = Node(pavement, name = 'pavement')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = BayesianNetwork('wet pavement model')\n",
    "model.add_states(s1, s2, s3)\n",
    "model.add_edge(s1, s2)\n",
    "model.add_edge(s1, s3)\n",
    "model.add_edge(s2, s3)\n",
    "model.bake()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "here's how our probabilistic [DAG](https://en.wikipedia.org/wiki/Directed_acyclic_graph) looks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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sWLECUqlUZx5gn8XDwwMSiQR//fWX2KbUCS56HaDkuSCrBQUFWL58OT755BNYiB2DvhosLS3h7Oyst6IXO9eUYeecekr79u1JIpHQ+PHj6ezZs2RlZUWzZs0S26yXsmbNGmrYsCGVlZWJbcrLqFZvvKXXAe7fvw8iQkREBHr06IEnT57A29tbbLNeioeHBwoLC3HhwgWxTVEZLnqRyc3NRWFhIQCgvLwcAOvueHl5YdiwYTh58qSY5tXIq6++CgsLCyQkJIhtispw0YvMnTt3XthXIf5Dhw7htddew82bN7Vt1t8ilUrRvXt3nD17VmxTVIaLXmSqE30F5eXlkEgkaNOmjRYtqj09evTgoueoTlpaGoxqSE4mlUrh5+dX4/ti06NHD1y6dElsM1SGi15k7ty5U+0cealUCn9/f50OnNq9e3e9jHGpm02IAREbG1tFOFKpFOPGjcPGjRtFn0r8d3Tu3Blubm5im6EyvKUXmWf79FKpFOPHj8emTZt0XvAVdOrUSWwTVIaLXkQUCgUyMjIAMMG/88472Lhxo6hLAlXl1VdfFdsEldGfs1sPefDgAeRyOQBgwoQJWL9+vV4JHmAtfX5+vthmqIR+neF6xrNdm19//VXvBA+wlv7KlStim6ES/EH278jJAdLS2Hb3LnDvHnDjBpCdXbk9ecLSzJeVVf4tk7GExMbGla+tWwNNm7LN0hJ3Hj4EAAQOGgTJ3bvAK6+w9PV6hKOjIzZv3qxXD7SGu0aWCEhJAVauBE6dAhITK8VakRK+Y0egTRvA1hawswMaNxbUhFOnTqFXr16QyOXAyZPsorp5E7hypXLLzWU2uLkB7u5s69lTcFvUYdy4cbrqWuVh/XD7NnD4MNtiY4HMTCYiNze29ezJhG5iohVzasWDB8DatezCPHWK/W9kxOz99lugd2/R7e3VqxdOnz4tqg01YKCiJwJmzgR++w24fh0wMwNefx3w8gI8PZl49Il794Djx4GYGHYxNGoEvPEG4OcHvPUW0KSJ1k2ytLRETk6O1uutBQYm+rNngY0bgZ07WUs4ejQwfDjg4SF6yygYt24BBw8Cu3axO5dEwi6AMWOASZO0ZoZEIkFWVhaaN2+utTprSfVBP2uaaK/lTRjy8ohWrybq0YMIIOrYkeiLLwQrXqfJzibauJFo5EgiY2OikBCixEStVA2ATp48qZW6VKRavYktduFE/8knRI0aETVsSDRxItHx44IUq5c8fEjk5MR+3j59iPbu1Wh1RkZGtH37do3WUUfq6cqpW7eADz4A/vc/YOFC4P59YMMGoF8/sS0TDysr5vk5ehSwtGTduu7dgYgI9owjMLa2trh165bg5WoK/ezTb9gAhIYyL8aXXwJTpzJXI+flJCUBs2YBFhbAsmVAq1aCFDt58mQ8fPgQ0dHRgpQnIPUgrF96OuDjAwQGAu+8w/zsQUFc8LWlc2dg717gxAn29//+J0ix9vb2L10Mo2vol+hdXYFr14C4OODf/2YtFkd1Ll5kHp633wZCQtignBrY2Njg7t27AhmnefRH9GvWAAMHAmfOMLcjp+40agT8+CMQGQls3gx4ewOPH9e5OFtbW+Tl5aGgoEBAIzWHfoj+u+9YN2b7dp0aftd7fH2Bv/5iI9UDBwJPpzmrirW1NQAWykQf0H3Rr1wJzJ7NWiaO8HTqxLqLxcWsxa8DrZ4+ED98OoFO19Fd0WdmAi1bsvkmCgUQHCy2RfUXW1vg6lXg55+BpUtVPvyVV15B06ZNcfnyZQ0YJzy6K/oZMwBzc+A//xHbkheIiopC27Zta51pLz09HevWrcPMmTNr/Mz8+fPRvXt3LFy4UCgzVcfdHZg/H6iDJ6Zp06Z4rMZzgTbRTdEnJQFbtgDff8+Er2PcunULqamptR6QuXPnDk6cOPHSrHwVSZFFHzextga++krlw5o2baqrk85eQDdFv3Ilm+Lr5ye2JdXyySefIDU1FR988EGtPu/u7v63ceYDAwOFME19Zs5kHh0VW20zMzMUFRVpyChh0T3RE7GZkZMmsVmDOoqqUcf+LmCTzgR0Cghgv8HevSodZmpq+kLIcV1F90SfnMweYgWO2hsZGYnx48dj6NChCAkJwYEDBwAAs2fPxooVKxAVFYWAgAD06dMHixcvBsDC6u3duxe+vr5ITU1FaGgohgwZgitXrmD+/PlYs2aNsvwzZ84gLCwMiYmJCA4OhqenJzZt2lStLbGxsQgJCUFwcDCCg4Nx/PjxGu3+7bffMHToUMydOxe5ubnK/ampqfj++++V2f6WL18uxGli3UkPDzZnXwX0SfRiz658cZblrl1sdmBxsWBT7eLj46lZs2aUlZVFRUVF5OXlReHh4XT06FECQE2bNiVXV1cKDAykpk2bEjstRAEBAQQ2L4h69OhB9vb2BIBcXFwIAM2dO5eIiJKSksjDw4MAUJcuXWjChAlkaWlJUqlUOeX22rVr9N577xER0f3796lNmzY0Z84cunPnDhERHThwgADQggULlHbPmzePBgwYQGvWrCFjY2NycnKiwsJCiomJITs7O3J2diZHR0cyNjambt26CXa+KCSE6PXXVTpk9OjRNG7cOOFsEAY9mVq8fTuRVEqkUAj2zdevX08AqG3btrR7925SKBSUn5/PzgpAwcHBVT4/ceJEio6OJiKi8ePHEwBKTU1Vvh8TE1NF9ERE9+7dU14sRKS8oGbPnk1ETPRdu3YlCwsLOnDgwAs2Pi/6GTNmEADq2bMn9ezZk5ydnaldu3b03XffERFRSkoKTZkyRYjT8yIzZhC5ual0iL+/P40ZM0Yz9tSdavWmIx3JZ2jThvnlb98GHBwEKXLs2LE4evQo1q9fj5EjR8Lb2xubN2+GeQ2eIUdHR6UnoiIsh6oRx6r7fEUCg3Xr1v1t0oWUlBRYWFjUuPZUKpVqLgrajRuAvb1Kh5SUlMDS0lIz9giM7vXpu3YFTE2BP/4QrMjy8nL8+uuv2L59O2xsbHDw4EG8/fbbNX4+OTkZHTp0EKz+CqZMmYJBgwZhx44dWLFixUs/27BhQ+Tl5SElJaXKfo3PW1cogPh4ldcOFxcXw9TUVENGCYvuib5RI7Zge8cOwYoMCQlBeno6xo4diwsXLsDV1RXHjh2rcTDl6NGjcHFxEaz+CmQyGbZu3YrWrVsjNDT0pQmIXV1dAQBz585V7ouPj8esWbMEt6sKR46wOTgjRqh0WElJCRe9WgQFAb//Dgg0rC2Xy7Fy5UoAQLNmzfDaa6+hc+fOyttxbGyscoZgREQEHj58CJOni8crcqU+mw0kLy8PQNUIZenp6VXqTE1NBQDlhZWVlYXc3Fy0bt0a27Ztg0KhgJ+fH86fPw+gcrJWRWzLoKAgNG7cGDt37sTq1avx0UcfISAgAMuWLVPapZEMJeHhLFqEijEqS0pKdCqz+UupqbOv5a0qCgVRt25EQ4cK8jQTEBBAFhYW5OvrS4GBgTR06FD6888/2ZMOQHZ2duTo6EgeHh7UvHlzWrVqFcnlcho3bhwZGxsTAOrQoQP98ssvRETk6OhIAMjCwoJmzpxJN27cIDc3NwJAn3/+Of3555/k4OBAAKhJkyb08ccfk6urKxkZGdGnn35KSUlJSk+QsbExvf/++2Rra0sAyNLSksLCwoiIeZ2sra0JANnb21NsbCwREUVFRZGzszPJZDLy9/enjIwMQc7T0xNCdOiQyoc5OzvTl19+KZwdwqAn3psK4uKIJBKitWvV/uZFRUVExDwsmZmZVd7DU+9Nbm4upaSkkFwuV7s+IVEoFHT9+nVSCOjNqpGcHCJ//zod2qpVK1qxYoXABqlNtXrTze4NAPTty2JDRkayhc7JyXUuquK2a21tjRYtWrzw/r1792BhYYGOHTvqXBBViUSCdu3aQaLJ0WmFApgyBbCxYYvHVSQ7OxsPHz6Es7OzBowTHt36hZ9HJgP++1/WvxwwQPDif//9dwAsi9+UKVOU/WmDoqwMmDCBLdCJjKxTERXz6FsJtNBc0+ien/55GjYEoqMBf3+2kNnfX7CiBw4cWGXmo774mQUjM5Odz/PngX37mNesDjx48AAAm1evD+i+6AEm/D17WMiPadPY8kEBPAUNGjTQH4+D0MTGAu++y1zEf/7JoiPUkXv37sHExKTarqMuotvdm2eRyZjvftMmFhUhLk5si/SXkBAW87JfP7bQXg3BA8Ddu3dhY2Oj2ecOAdEf0QMsbMWlS0D79kD//sDkySyiGad2KBQsqG1EBFuks2OHIGFU0tLSYGdnJ4CB2kG/RA8wD8PevewH/Okn9sNZW7PWS49Cy2mFsjIWDa5TJ3anHDeOTS/IyADGjxesmmPHjmGABhwNmkL/RP8spqbAZ5+x7B379gEdOrCwFvv2AU8TmBks8+ezCXvvvceEnpRU6QkTmNu3b6Nt27aCl6sp9Fv0FTRowCKfbdkC5OWxeSP29sC8eaw7ZCjk5bFz8OabLGHD5MksEcWGDYAGfehPnjyBo6OjxsoXGv0M4Pp3XL8O/PILW+t57x6LmzN6NNCrl04vQawTWVnA7t3Mx374MFvq5+3NMq9oaQmiRCJBamqqyksotYCBZSIBmABOnGD919RUNrLr6clS73h5CTZfX+sUFjLvVVgYcO4cy1zo7c0W0o8cycJzaxFTU1MUFRXp3Gg2DFL0z3LuHHDoEGsN4+KAoiLWBZo2jfV5e/TQyXAjAFh05opEa6dOMTdjaWml69HLS9Rwh87OzrqaS9bARf8sJSVsocQff7BgUhkZgFTKwo506sT6v76+7H9tRkaWy9kdKTm5MqVmcjIbPDI2Zgts3N1ZRkFPTxaZTAcYPnw49qoYPUFLcNGrxNWrbNncs4mT09LYuMCNG+qFt5ZIAAsL3G3cGCEFBVjTty+sBg1iuWrt7QEnJ613UdThP//5D0JCQsQ2ozqqFb1+TEMQg44d2VYTT56wbOLZ2UBBAfOJl5ay/WVl7M5hYlI1a3irVsps4ZBK0byoCAkODljauTOWzJihve8mIJmZmXBychLbDJXgLb3IfP/991i4cCHy8/PFNqVO/PHHH3B0dISNjY3YplRHPUi/Uw8JDg7Wm7Wl1ZGcnKyrgq8RLnqRMTc3x6effqpcd6tvJKuxuEcsuOh1gGnTpuGHH34Q24w6cfHiRbFNUBnep9cRzM3NsWDBAoSGhoptSq158OABrK2toSMaqg7ep9dlgoODsXTpUhQXF4ttSq2pCF+ib3DR6wihoaHIzc3FL7/8IrYptebMmTOwVzH8ny7ARa8jtGrVCu+99x6WLFmCUjXzumqL06dPo1evXmKboTJc9DrEzJkzkZGRgQ0bNohtSq3goueoja2tLSZPnoxvvvkG5eXlYpvzUtLT03H37l0ueo76zJ49G2lpadi6davYpryUhIQESCQSvRQ9n3ujYzg4OCApKQmvvvoqTE1NMXbsWLFNqpalS5di6tSpehkriLf0OkjHjh0xZswYLFq0SCd94GVlZTh9+jQ8PDzENqVOcNHrKHPnzsWlS5ewe/dusU15gXPnzqGoqAh9+vQR25Q6wUWvo3Tp0gWjRo3C119/LbYpL3Ds2DFYWVnpTcDW5+HTEHSYs2fPomfPnjrXxRkxYgQaNGiAiDpEONYyfBqCvtGjRw8MGzZMbDOqoFAoEBcXh/79+4ttSp3hotdx5s2bh9jYWLHNUHLhwgXk5OToteh590YPkEgkiIuLQ9++fcU2BT4+PmjYsKE+dG0A3r3RX/r27asTD7Tl5eU4fvw4vLy8xDZFLbjo9YD58+fj999/rzGRsrZISEhAQUEBFz1H8wwePBhubm6it/aHDh1CmzZtNJJYWptw0esJ8+bNQ1RUFC5cuCCaDdHR0RgyZIho9QsFf5DVE4gIrq6ucHZ2xg4Bs6mrgkwmQ2RkJEaOHClK/XWARzjTdxQKBTp37gw3Nzds3LhR6/V7eXkhJiZG6/WqAffe6DtSqRRz587Ftm3bcPPmTa3WrVAoMHToUK3WqSl4S69nyOVyODk5YdCgQVizZo3W6k1ISIC5uTk6q5mUTcvwlr4+IJPJMHv27Gq7NyUlJYLU8dtvv2Hv3r1VyouOjtY3wdcIF70eMmnSJLRu3Vqw5HrvAAAO2klEQVT5//379/HZZ5+hX79+gpQfFxeHESNGoGnTphg7diwiIiKwZ88eQcrWCYhIFzaOiqxcuZJOnjxJH374IRkZGREAatiwoSBlh4WFkbGxMQEgIyMjkkgkJJVKaf369fTo0SNB6tAS1eqNLxfUUwYOHIiuXbtCKpUqF5EXFhYiLy8PFmomkjA1NVUmQq4om4gQGBgIAOjfvz/Gjh2LoKAgXUy587fon8UGSlZWFvz8/CCRSGBsbIwuXbpAoVC8EDUhToBM6o1rSOWjUCgglUqRn5+PqVOn6qXgAS56vaFFixawfZpup6bwIEZGRrhz547adZmamla7cEUikcDMzAyRkZEwNjZWux6x4KLXI5YvX45PP/1U2fV4HqlUirS0NLXrMTU1hUKheGE/EWHbtm26mDpTJbjo9Yxly5bVKPzy8nJBWnoTE5NqW/pZs2bBx8dH7fLFhoteDwkPD8f06dNf2K9QKHD9+nW1y6+upTcyMhJ9lqdQcNHrKf/617+q3Z+amqp22c+nA5JKpTA3N4eRljKQaxouej2GiBAWFlZl34MHD3D//n21yn3We1Mx3yc7O1utMnUJLno9Z9GiRZg3b16Vfer26ytaeplMhr59+2LBggVqladrcNHXA7766it88cUXyv/VFb2JiQkAwNLSEhEREXrrj6+J+tFJM1TkciA9Hbh3D1927w7J0KH4MjoaacuXA5s2seTOOTlAfj5L7FxWxrbCQqC8nCV1fn6zsoKpTAYpgIiePdHqm29Ywmdra8DNDbCxAVq0YFnP9RQuen1ALgdu3ACuXq26HT/O3nvKgubNIbWywp3bt4F27QAHB5ad3MKiMnO5sTHQsCFgZFR5EVRspaVARgZMb93Cl2VlGGRkBJw6BTx6BNy/zy4egJVlZ1eZVX3ECPZqZyfO+VERPp9eFykvBy5dAs6eZduvv7LWGQBat2YC69AB8PZmLbCNDXt92hc/efIk3N3d61x9cXExTExMXuzWpKQA9+6xC+DmzcqL79Qp9n6zZkCPHlU3cReR8+WCOs2ffwLHjgFHjwLx8cCTJ4CZGdC1KzB1KtC9O+DkBNQwL0ZUMjOB5GR2gZ47x16vXGEXr58fMHAgMGAA0KWLtrtFXPQ6wY0bwNatwO7dwJkzrKvxxhvA0qVA+/ZiW6cZFAogMRGIiQH27GEXtVQK/PvfwNixQPPmmqqZi15U8vIAHx8gLg6wsgJGj2Z9YU9PoEEDsa3TLo8fA9HRQFAQuxv4+ACTJgHDhrFnDuHgywVFITERCAxkfXEbG2DfPtYvXrWK/ciGJniA9f3feQd4+BD4+WfWIIwezc5PWBhw965Gq+ctvaaIiQG++Ya9dukChIQAH34otlW6y927wC+/sIsgMxM4fx7o1EndUqt/gKhpSZWWt/rDH38Q9etHBBC9+SbRoUNiW6RflJYSbdhAJJUSBQQQXb+uTmnV6o13b4QkNRXo14+5Dv/6Czh4kD2kcmqPsTEwcSKwfTvzBHXqBMycWTlGIAQ1XQ1a3vQbuZxo2TKiRo2IoqPFtqb+UF5OtGoVUfPmRHZ2RHv3qloCb+kFJy6OPaC6uACDBgEFBUA9CHCqM8hk7DkoKwu4c4d5epo3Z3dUNeCirysREYCXF9C/P3DyJNCtm9gW1X9GjmQDXx4egBrRm7no68KOHcC4ccC0aezvRo3EtshwsLevvLPWUfjcZVkXjI2B6dOBJUvEtsQwKSkB3nqLif7UKeBplIhq4COygvDgARAaCmzZIrYlhk1+PvD662x+UlwcmzX6InxEVhA+/JANoHDEpXFj4L//BS5eBGpYL1wTXPSqMGwYm/3I+/Aqo1Ao4OnpCfkz8//VxsmJeXaWLgUWLqz1YVz0tSUriw028akEdSIsLAxHjhypNp6OWpiZscGsrVtrf0xNDnwtb7rP//7Hhsbz8wUrMjc3lzZt2kRvvfUW/fOf/6Q+ffqQv78/nT9/XvmZx48fU0BAAPXq1Ys++ugjyn9a/40bN2jUqFHk6+tLO3bsICKi5ORkGjt2LI0aNUp5/K5du2jSpEk0ZMgQCgsLo5ycHFIoFBQXF0dBQUF07do12rx5M40dO5amTZtG5eXlFBERQQEBATRx4kQ6c+aMsqyMjAyaO3cu+fj40Lhx4yj66UBcdnY2bdq0iXx9fenOnTu0YsUKevPNN2nKlClERDRnzhwCe26jiRMnUlhYmGDnkIiIYmLYtI97955/p1q9iS12/RH9V18RtW8vaJH/+Mc/qEGDBgSAxo8fT/379ycA1KhRI7p58yYREQ0ePJhKS0spKSmJLCwsaMKECcrjAZC9vX2VMmfMmKEU/bx582jAgAEUFxdHa9asIWNjY3JycqJvv/2WmjRpQgDI1dWVfH19KSQkhKRSKQ0bNoxGjBhBQ4YMIQDUqlUrksvlRETUrl07Wr16Nf355580cOBAAkBr166lRYsWkbm5OQEgZ2dn8vPzoz59+hBrU4lOnDhBTk5OBICOHDlCJ06cEPQ8UmYmk/Lhw8+/w0WvFjNmELm7C15shXgqCAwMJAD0wQcfUGFhIZmamirf69WrF7V/5sLz8vIiAJSQkKDc1717d/rrr7/o3LlzJJPJ6M6dO8r3Bg8erKxr+vTpBICWLVumfP/dd9+lFStWKP+fNGkSAaDU1FQiIpo6daryvb/++osA0CuvvKI8FgCtX79e+RkrK6sqtkskkjqcoVoglzMpR0Q8/061euMLw2uLmRlQVCR4sY2eeyieN28e1q1bh8TERJiZmSEpKQl5eXnYtGkTrl27huLiYuVnP/74Y8TExOCnn36Cu7s7zp49C4VCgd69eyM0NBRyuRy+vr7Kzz958gTt2rUDADRp0gQA4OLionzfyckJXbt2Vf7v7OwMgEVNa9q0KXbu3InExEQALPdVu3btlOtozczMqhwDAJ06dUJJSYkyjk5NgWfVpuJ3eWrD38FFX1scHNhSP4WCLXXTEPb29pBKpcjJyQEAWFlZoV+/fvjss8/g7OysFB0AjBgxAnZ2dti+fTvCw8OxZs0afPDBBwCAlJQUWFhY4PTp07Wuu8FzC1oqwnGXlZXh6tWrmD9/frUxNGtCJpNV+V9jor92jb06ONTq49x7U1sCA4E2bYCPP9ZoNT/99BMUCgU+/fRTREREwMLCAomJiZg0aRLKysqqeD9kMhlOnz6N8vJyWFpaoqysDMHBwQCAPn36IC8vD/7+/lWOiY+Pr7HuZz/3PC4uLpg5cybOnTun3KdQKODv71+r7yWRSKpNIiEIgYHA5Mm1XnTCRa8KH38MrF+vseKfPHmC9evXw9nZGVOnTlWm0YmKikJYWBjOnj2L0tJS7Nq1CxcvXgTA7gRvv/02AChbeQAICgpC48aNsXPnTnh7e2P16tX46KOPEBAQAIDFvASA3Nxc5TGPHj2qEt8+KysLAJCdnQ0TExPI5XIMGDAACxYsQHh4OPr16weHp61renr6C+Wlpqbi0aNHAABra2sQEdauXYt169bh8uXLwpy06Gg2716Vxqimzr6WN/2gpITI0VHQIn18fAgAubu7k62tLfXr14/S09OJiEgul5OPjw/Z2NjQ4sWLafny5SSVSqlr1650+/ZtZRnx8fHUvXv3F8qOj48na2trpbvQ3t6eYmNjKTw8XOm9cXFxoX379tE333xDTZo0ITs7O9q+fTv98MMP1KJFCwJAHTt2pF27dtHUqVNJKpUSAJJIJBQUFESFhYW0ZMkSMjMzIwDUrVs3SkhIoKCgIAJAAwcOpKysLNqyZQtJJBKSSCQ0ffp0UigU6p+8wkKijh2J/P1r+gT33ghCTAzR2rWCFVch+hs3blBWVtbffj43N7fa/ZmZmdXuVygUdO3aNbp+/bogQsvPz6dz585RXl6eysdmZmYKm53w/feJmjatzj9fARe9YJiYEB05IkhRFaLnqMjSpWywcM+el32qWr3xPn1dePttYPhwFpFMTSr6vBwVWLmSzXT997/Z76AiXPR1YfNmNrV1717mvgwNZQFQVSQnJwfR0dHIzs6u4n/n1MCjRywwlKUlcx1Pm1anYvh8enXZupVNQuvQAdiwgcW44QjPvn3A+++zSBO3btX2KD6fXiMEBDCXmZkZi9JbUCC2RfWLu3eBMWNYN8bbmwWBUhMueiFo1w744w9g+XLW4v/8c526O5xnyMkB5s1jYckTE4EDB9gYydOxC3Xg3Ruh+eQTYPVqFpdxzhw21/u5bH2cv+HRIxbBWSZjsS2nTatrYFfevdEKy5ezuSDe3uzHatuWrep5OmLJeQlJScBHH7HpHtOns8QP06cLHcmYt/Qa5cED5l77+WcgN5eFqhs+nKWv4TCys9la102bWGKKDh1YY1FHz8xz8GgIonPvHvtxt25lC5qbNGER0UaMYKGr6zu3bzM37549LOOKhwcwYQJ7UNVMhhUuep3i1i0gKoptx4+zAEb9+1duLVqIbaEwbNjABvGOH2dTs83NgcGDWdyaiRM1XTsXvc6SkwMsWMBav4sXASK20r9nT+YGDQxkAzK6zv37VfNOnT7NYs27u1fmnXr9dW0+2HPR6wXZ2cz9mZDAclKdPcuE07Yt4OzM+rwVqSw9PWsKcqRZiovZneraNZZdcN8+4PJlICODvd+2LbtYe/ZkD6LiZVvhotdboqLYHaAihWVKCrs4pFKgVauqaTWtrVmy47Zt2TPD83lkTUxYcjeZjEUBrsgfW5FLNiOjMulyTg57AH/0iD2PnDrFWvNn5wtZW7OHcycnFsS2Rw9Wv27ARV+vyMoCjhxhYqzY7t9nHqOcnMpWVx3MzNhF06wZ8MorrJtScXHZ27O7jrm5+vVoDi56g6KoqLK1zs+v2qIXFrJM40ZGlVnEK+4CLVsyoTdpUh9cq1z0HIODj8hyOAAXPccA0ZW4NxoKiMLhvAhv6TkGBxc9x+DgoucYHFz0HIODi55jcHDRcwwOLnqOwcFFzzE4uOg5BgcXPcfg4KLnGBxc9ByDg4ueY3Bw0XMMDi56jsHBRc8xOLjoOQYHFz3H4OCi5xgcXPQcg4OLnmNwcNFzDA4ueo7B8X+WSkKsg2nfkQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "what's really cool about BNs is that they enable inference with partial information (incomplete data)\n",
    "\n",
    "suppose we observe that the pavement is wet and we know that it didn't rain today, what's the probability the sprinkler was on? we can calculate this by hand with [Bayes' theorem](https://en.wikipedia.org/wiki/Bayes%27_theorem) or we can have pomegranate do those calculations for us:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['No'\n",
      " {\n",
      "    \"class\" :\"Distribution\",\n",
      "    \"dtype\" :\"str\",\n",
      "    \"name\" :\"DiscreteDistribution\",\n",
      "    \"parameters\" :[\n",
      "        {\n",
      "            \"On\" :0.9966777408637874,\n",
      "            \"Off\" :0.0033222591362126854\n",
      "        }\n",
      "    ],\n",
      "    \"frozen\" :false\n",
      "}\n",
      " 'Wet']\n"
     ]
    }
   ],
   "source": [
    "print(model.predict_proba(['No', None, 'Wet']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "99.7% probability that the sprinkler was on. suppose we didn't know whether it rained but we knew for sure that the sprinkler never turned on, we can similarly calculate the probability that it rained:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{\n",
      "    \"class\" :\"Distribution\",\n",
      "    \"dtype\" :\"str\",\n",
      "    \"name\" :\"DiscreteDistribution\",\n",
      "    \"parameters\" :[\n",
      "        {\n",
      "            \"Yes\" :0.9940298507462686,\n",
      "            \"No\" :0.0059701492537314734\n",
      "        }\n",
      "    ],\n",
      "    \"frozen\" :false\n",
      "}\n",
      " 'Off' 'Wet']\n"
     ]
    }
   ],
   "source": [
    "print(model.predict_proba([None, 'Off', 'Wet']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "99.4% chance that it rained"
   ]
  },
  {
   "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}