capitulo3_distribuições (incompleto).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bibliotecas e Módulos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot\n",
    "from empiricaldist import Pmf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from os.path import basename, exists\n",
    "\n",
    "def download(url):\n",
    "    filename = basename(url)\n",
    "    if not exists(filename):\n",
    "        from urllib.request import urlretrieve\n",
    "        local, _ = urlretrieve(url, filename)\n",
    "        print('Downloaded ' + local)\n",
    "    \n",
    "download('https://github.com/AllenDowney/ThinkBayes2/raw/master/soln/utils.py')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from utils import set_pyplot_params\n",
    "set_pyplot_params()\n",
    "\n",
    "from utils import decorate\n",
    "\n",
    "def decorate_bowls(title):\n",
    "    decorate(xlabel='Bowl #',\n",
    "             ylabel='PMF',\n",
    "             title=title)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A classe `Pmf` representa uma função massa de probabilidade. No exemplo abaixo, `coin`se trata de uma moeda, e por se tratar de um espaço amostral discreto, podemos determinar todos os seus elementos e as suas probabilidades associadas. E isso é feito através da atribuição de valores às linhas `heads` (cara) e `tails` (coroa)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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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",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Pmf([], Name: , dtype: float64)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</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>heads</th>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tails</th>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "heads    0.5\n",
       "tails    0.5\n",
       "Name: , dtype: float64"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# construção da pmf sem atribuição de valores\n",
    "coin = Pmf()\n",
    "display(coin)\n",
    "\n",
    "# atualização do DataFrame que representa a pmf\n",
    "coin['heads']=1/2; coin['tails']=1/2\n",
    "display(coin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No exemplo abaixo, construímos a pmf associada aos resultados do lançamento de um dado equilibrado de seis faces."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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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>1</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "1    0.166667\n",
       "2    0.166667\n",
       "3    0.166667\n",
       "4    0.166667\n",
       "5    0.166667\n",
       "6    0.166667\n",
       "Name: , dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "die = Pmf.from_seq([1,2,3,4,5,6])\n",
    "die"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "É permitida a computação das probabilidades referentes à valores repetidos na sequência inserida no método `from_seq`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</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>M</th>\n",
       "      <td>0.090909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>i</th>\n",
       "      <td>0.363636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>p</th>\n",
       "      <td>0.181818</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>s</th>\n",
       "      <td>0.363636</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "M    0.090909\n",
       "i    0.363636\n",
       "p    0.181818\n",
       "s    0.363636\n",
       "Name: , dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "letters = Pmf.from_seq(list('Mississippi'))\n",
    "letters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pode-se utilizar a indexação dos elementos para recuperação de valores, ou também chamar o objeto Pmf, tal qual uma função."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.36363636363636365"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "letters['s']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.36363636363636365"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "letters('s')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observe que enquanto função, é permitida a verificação de valores ausentes do espaço amostral, já utilizando os colchetes de indexação, é retornado um aviso de erro."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "letters('t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "KeyError",
     "evalue": "'t'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32mC:\\Leonardo\\Programas\\Anaconda\\lib\\site-packages\\pandas\\core\\indexes\\base.py\u001b[0m in \u001b[0;36mget_value\u001b[1;34m(self, series, key)\u001b[0m\n\u001b[0;32m   4410\u001b[0m             \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 4411\u001b[1;33m                 \u001b[1;32mreturn\u001b[0m \u001b[0mlibindex\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_value_at\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ms\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   4412\u001b[0m             \u001b[1;32mexcept\u001b[0m \u001b[0mIndexError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.get_value_at\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.get_value_at\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\util.pxd\u001b[0m in \u001b[0;36mpandas._libs.util.get_value_at\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\util.pxd\u001b[0m in \u001b[0;36mpandas._libs.util.validate_indexer\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;31mTypeError\u001b[0m: 'str' object cannot be interpreted as an integer",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-10-b09f4b231f49>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mletters\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m't'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32mC:\\Leonardo\\Programas\\Anaconda\\lib\\site-packages\\pandas\\core\\series.py\u001b[0m in \u001b[0;36m__getitem__\u001b[1;34m(self, key)\u001b[0m\n\u001b[0;32m    869\u001b[0m         \u001b[0mkey\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcom\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mapply_if_callable\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    870\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 871\u001b[1;33m             \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_value\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    872\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    873\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mis_scalar\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Leonardo\\Programas\\Anaconda\\lib\\site-packages\\pandas\\core\\indexes\\base.py\u001b[0m in \u001b[0;36mget_value\u001b[1;34m(self, series, key)\u001b[0m\n\u001b[0;32m   4417\u001b[0m                     \u001b[1;32mraise\u001b[0m \u001b[0mInvalidIndexError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   4418\u001b[0m                 \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 4419\u001b[1;33m                     \u001b[1;32mraise\u001b[0m \u001b[0me1\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   4420\u001b[0m             \u001b[1;32mexcept\u001b[0m \u001b[0mException\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   4421\u001b[0m                 \u001b[1;32mraise\u001b[0m \u001b[0me1\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Leonardo\\Programas\\Anaconda\\lib\\site-packages\\pandas\\core\\indexes\\base.py\u001b[0m in \u001b[0;36mget_value\u001b[1;34m(self, series, key)\u001b[0m\n\u001b[0;32m   4403\u001b[0m         \u001b[0mk\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_convert_scalar_indexer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkind\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m\"getitem\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   4404\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 4405\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_engine\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_value\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ms\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mk\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtz\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mgetattr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mseries\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"tz\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   4406\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   4407\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;32mand\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mholds_integer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_boolean\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_value\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_value\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.hashtable.PyObjectHashTable.get_item\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.hashtable.PyObjectHashTable.get_item\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;31mKeyError\u001b[0m: 't'"
     ]
    }
   ],
   "source": [
    "letters['t']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tal qual um objeto `Series`, é possível verificar diversos valores simultâneamente"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.16666667, 0.16666667, 0.        ])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "die([1,4,7])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Nova resolução do exemplo 1 do capítulo 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Construção das probabilidades a priori por meio do objeto Pmf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</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>Bowl 1</th>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bowl 2</th>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Bowl 1    0.5\n",
       "Bowl 2    0.5\n",
       "Name: , dtype: float64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prior = Pmf.from_seq(['Bowl 1','Bowl 2'])\n",
    "prior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Utilizando o léxico do Teorema de Bayes: acabamos de construir a distribuição a priori do problema, pois se trata da probabilidade das hipóteses sem a verificação dos dados."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Abaixo temos as verossimilhanças e atualização da planilha a partir da observação dos dados, tendo conhecimento das hipóteses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</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>Bowl 1</th>\n",
       "      <td>0.375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bowl 2</th>\n",
       "      <td>0.250</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Bowl 1    0.375\n",
       "Bowl 2    0.250\n",
       "Name: , dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likelihood_vanilla = [0.75,0.5]\n",
    "posterior = prior*likelihood_vanilla\n",
    "posterior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finalizamos com a construção da distribuição a posteriori por meio da normalização das probabilidades calculadas anteriormente.<br>\n",
    "O valor retorno é a probabilidade dos dados observados, sem levar em consideração as hipóteses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.625"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior.normalize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</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>Bowl 1</th>\n",
       "      <td>0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bowl 2</th>\n",
       "      <td>0.4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Bowl 1    0.6\n",
       "Bowl 2    0.4\n",
       "Name: , dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 101 tigelas!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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