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    "# This tutorial on using Bayesian network to solve the Monty Hall problem is originally from the following link:\n",
    "# https://www.edureka.co/blog/bayesian-networks/\n",
    "#\n",
    "# Addiitonal comments in the notebook added by Yuanpeng Zhang @ Wed 18-Dec-19.\n",
    "#\n",
    "\n",
    "# Import required packages\n",
    "import math\n",
    "# The following module can be installed with conda 'conda install pomegranate'.\n",
    "from pomegranate import *\n",
    " \n",
    "# Initially the door selected by the guest is completely random\n",
    "guest =DiscreteDistribution( { 'A': 1./3, 'B': 1./3, 'C': 1./3 } )\n",
    " \n",
    "# The door containing the prize is also a random process\n",
    "prize =DiscreteDistribution( { 'A': 1./3, 'B': 1./3, 'C': 1./3 } )\n",
    " \n",
    "# The door Monty picks, depends on the choice of the guest and the prize door\n",
    "monty =ConditionalProbabilityTable(\n",
    "[[ 'A', 'A', 'A', 0.0 ],\n",
    "[ 'A', 'A', 'B', 0.5 ],\n",
    "[ 'A', 'A', 'C', 0.5 ],\n",
    "[ 'A', 'B', 'A', 0.0 ],\n",
    "[ 'A', 'B', 'B', 0.0 ],\n",
    "[ 'A', 'B', 'C', 1.0 ],\n",
    "[ 'A', 'C', 'A', 0.0 ],\n",
    "[ 'A', 'C', 'B', 1.0 ],\n",
    "[ 'A', 'C', 'C', 0.0 ],\n",
    "[ 'B', 'A', 'A', 0.0 ],\n",
    "[ 'B', 'A', 'B', 0.0 ],\n",
    "[ 'B', 'A', 'C', 1.0 ],\n",
    "[ 'B', 'B', 'A', 0.5 ],\n",
    "[ 'B', 'B', 'B', 0.0 ],\n",
    "[ 'B', 'B', 'C', 0.5 ],\n",
    "[ 'B', 'C', 'A', 1.0 ],\n",
    "[ 'B', 'C', 'B', 0.0 ],\n",
    "[ 'B', 'C', 'C', 0.0 ],\n",
    "[ 'C', 'A', 'A', 0.0 ],\n",
    "[ 'C', 'A', 'B', 1.0 ],\n",
    "[ 'C', 'A', 'C', 0.0 ],\n",
    "[ 'C', 'B', 'A', 1.0 ],\n",
    "[ 'C', 'B', 'B', 0.0 ],\n",
    "[ 'C', 'B', 'C', 0.0 ],\n",
    "[ 'C', 'C', 'A', 0.5 ],\n",
    "[ 'C', 'C', 'B', 0.5 ],\n",
    "[ 'C', 'C', 'C', 0.0 ]], [guest, prize] )\n",
    " \n",
    "d1 = State( guest, name=\"guest\" )\n",
    "d2 = State( prize, name=\"prize\" )\n",
    "d3 = State( monty, name=\"monty\" )\n",
    " \n",
    "#Building the Bayesian Network\n",
    "network = BayesianNetwork( \"Solving the Monty Hall Problem With Bayesian Networks\" )\n",
    "network.add_states(d1, d2, d3)\n",
    "network.add_edge(d1, d3)\n",
    "network.add_edge(d2, d3)\n",
    "network.bake()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "guest\tA\n",
      "prize\t{\n",
      "    \"class\" :\"Distribution\",\n",
      "    \"dtype\" :\"str\",\n",
      "    \"name\" :\"DiscreteDistribution\",\n",
      "    \"parameters\" :[\n",
      "        {\n",
      "            \"A\" :0.3333333333333333,\n",
      "            \"B\" :0.3333333333333333,\n",
      "            \"C\" :0.3333333333333333\n",
      "        }\n",
      "    ],\n",
      "    \"frozen\" :false\n",
      "}\n",
      "monty\t{\n",
      "    \"class\" :\"Distribution\",\n",
      "    \"dtype\" :\"str\",\n",
      "    \"name\" :\"DiscreteDistribution\",\n",
      "    \"parameters\" :[\n",
      "        {\n",
      "            \"B\" :0.49999999999999983,\n",
      "            \"A\" :0.0,\n",
      "            \"C\" :0.49999999999999983\n",
      "        }\n",
      "    ],\n",
      "    \"frozen\" :false\n",
      "}\n"
     ]
    }
   ],
   "source": [
    "# Given the guest selecting door 'A', we update the probability of the network.\n",
    "beliefs = network.predict_proba({ 'guest' : 'A' }) # The returned value 'beliefs' here is a list.\n",
    "beliefs = map(str, beliefs) # Map the 'beliefs' list to 'str' function for printing purpose next.\n",
    "print(\"\\n\".join( \"{}\\t{}\".format( state.name, belief ) for state, belief in zip(network.states, beliefs)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "guest\tA\n",
      "prize\t{\n",
      "    \"class\" :\"Distribution\",\n",
      "    \"dtype\" :\"str\",\n",
      "    \"name\" :\"DiscreteDistribution\",\n",
      "    \"parameters\" :[\n",
      "        {\n",
      "            \"A\" :0.3333333333333334,\n",
      "            \"B\" :0.0,\n",
      "            \"C\" :0.6666666666666664\n",
      "        }\n",
      "    ],\n",
      "    \"frozen\" :false\n",
      "}\n",
      "monty\tB\n"
     ]
    }
   ],
   "source": [
    "# In previous situation, the guest selects door 'A' but monty hasn't selected the door yet. From the result above, \n",
    "# we know that the distribution of prize among the doors will not be influenced by the guest's choice, but the selection\n",
    "# of monty will. In this case, we go a bit further by specifying that monty also makes his/her choice to open the door 'B'.\n",
    "# In this case, the distribution of prize will for sure change, accordingly.\n",
    "beliefs = network.predict_proba({'guest' : 'A', 'monty' : 'B'})\n",
    "print(\"\\n\".join( \"{}\\t{}\".format( state.name, str(belief) ) for state, belief in zip( network.states, beliefs )))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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