{
"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": [
{
"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>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": [
{
"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>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"
]
},
{
"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": [
{
"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>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": [
{
"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>4</th>\n",
" <td>0.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>0.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>0.919294</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>0.080706</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
"4 0.000000\n",
"6 0.000000\n",
"8 0.919294\n",
"12 0.080706\n",
"dtype: float64"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dice"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"dice.update??"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
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"nbformat_minor": 4
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