{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from datascience import *\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plots\n",
    "plots.style.use('fivethirtyeight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Decisions ##"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# np.array(list) converts list to an array\n",
    "# provided all the elements of list are of the same type\n",
    "\n",
    "n = 100\n",
    "second = round(n * 0.6)\n",
    "third = round(n * 0.4)\n",
    "\n",
    "year = np.array(['Second'] * second + ['Third'] * third)\n",
    "major = np.array(['Declared'] * (round(second * 0.5)) + ['Undeclared'] * (round(second * 0.5)) + \\\n",
    "                 ['Declared'] * (round(third * 0.8))  + ['Undeclared'] * (round(third * 0.2)))\n",
    "                 \n",
    "students = Table().with_columns(\n",
    "    'Year', year,\n",
    "    'Major', major\n",
    ")\n",
    "students.show(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "students.pivot('Major', 'Year')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Chance of third year, given that they have declared\n",
    "# P(third year | declared) = 32/(30+32)\n",
    "\n",
    "32 / 62"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# P(second year | declared)\n",
    "\n",
    "30 / 62"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Bayes' Rule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Proportion of 2nd Years among students who are Declared\n",
    "(0.6 * 0.5) / ((0.6 * 0.5) + (0.4 * 0.8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Proportion of 3rd Years among students who are Declared\n",
    "(0.4 * 0.8) / ((0.6 * 0.5) + (0.4 * 0.8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Interpretation by Physicians of Clinical Laboratory Results (1978)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Problem did not give the true positive rate (it was assumed to be 100%)\n",
    "(0.001 * 1) / ((0.001 * 1) + (0.999 * 0.05))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 10000\n",
    "disease = round(n * 0.001)\n",
    "no_disease = round(n * 0.999)\n",
    "\n",
    "status = np.array(['Disease'] * disease + ['No disease'] * no_disease)\n",
    "result = np.array(['Test +'] * (disease) + ['Test +'] * (round(no_disease * 0.05))  + \\\n",
    "                 ['Test -'] * (round(no_disease * 0.95)))\n",
    "                 \n",
    "persons = Table().with_columns(\n",
    "    'Status', status,\n",
    "    'Test Result', result\n",
    ")\n",
    "persons.show(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Among the Test+ column, more people do *not* have the disease than do\n",
    "persons.pivot('Test Result', 'Status')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Number with \"No disease\"\n",
    "500 + 9490"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# P(Disease | Test +)\n",
    "10/510"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Using Subjective Prior Probabilities ##"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#P(Disease | positive), P(Disease) = .1\n",
    "(0.1 * 1) / ((0.1 * 1) + (0.999 * 0.05))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#P(Disease | positive), P(Disease) = .5\n",
    "(0.5 * 1) / ((0.5 * 1) + (0.5 * 0.05))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_population(prior_disease_prob, n):\n",
    "    disease = round(n * prior_disease_prob)\n",
    "    no_disease = round(n * (1 - prior_disease_prob))\n",
    "\n",
    "    status = np.array(['Disease'] * disease  +  ['No disease'] * no_disease)\n",
    "    result = np.array(['Test +'] * (disease) + ['Test +'] * (round(no_disease * 0.05))  + \\\n",
    "                 ['Test -'] * (round(no_disease * 0.95)))\n",
    "                 \n",
    "    t = Table().with_columns(\n",
    "    'Status', status,\n",
    "    'Test Result', result\n",
    "    )\n",
    "    return t.pivot('Test Result', 'Status')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "create_population(0.5, 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "5000 / (5000 + 250)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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