{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dice & German Tank Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import empiricaldist\n",
    "from empiricaldist import Pmf, Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Manual Way"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.25</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "4     0.25\n",
       "6     0.25\n",
       "8     0.25\n",
       "12    0.25\n",
       "dtype: float64"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dice = Pmf.from_seq([4,6,8,12])\n",
    "dice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.09374999999999999"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dice[4] *= 0\n",
    "dice[6] *= 1/6\n",
    "dice[8] *= 1/8 \n",
    "dice[12] *= 1/12\n",
    "\n",
    "dice.normalize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.444444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "4     0.000000\n",
       "6     0.444444\n",
       "8     0.333333\n",
       "12    0.222222\n",
       "dtype: float64"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def likelihood_dice(data, hypo):\n",
    "    if data > hypo:\n",
    "        return 0\n",
    "    else:\n",
    "        return 1 /hypo\n",
    "    \n",
    "    # Solution\n",
    "    \n",
    "# def likelihood_dice(data, hypo):\n",
    "#     \"\"\"Likelihood function for the dice problem.\n",
    "    \n",
    "#     data: outcome of the die roll\n",
    "#     hypo: number of sides\n",
    "    \n",
    "#     returns: float probability\n",
    "#     \"\"\"\n",
    "#     if data > hypo:\n",
    "#         return 0\n",
    "#     else:\n",
    "#         return 1 / hypo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.444444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "4     0.000000\n",
       "6     0.444444\n",
       "8     0.333333\n",
       "12    0.222222\n",
       "dtype: float64"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dice = Pmf.from_seq([4,6,8,12])\n",
    "dice.update(likelihood_dice, 6)\n",
    "dice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for roll in [8,7,7,5, 4]:\n",
    "    dice.update(likelihood_dice, roll)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.000000</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.000000</td>\n",
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       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.919294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.080706</td>\n",
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       "4     0.000000\n",
       "6     0.000000\n",
       "8     0.919294\n",
       "12    0.080706\n",
       "dtype: float64"
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     "execution_count": null,
     "metadata": {},
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   ],
   "source": [
    "dice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dice.update??"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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