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‎lec/lec37/lec37.ipynb‎

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"from datascience import *\n",
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"import numpy as np\n",
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"import matplotlib\n",
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"from mpl_toolkits.mplot3d import Axes3D\n",
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"\n",
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"%matplotlib inline\n",
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"import matplotlib.pyplot as plots\n",
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"plots.style.use('fivethirtyeight')\n",
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"\n",
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"import warnings\n",
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"warnings.simplefilter(\"ignore\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# np.array(list) converts list to an array\n",
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"# provided all the elements of list are of the same type\n",
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"\n",
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"n = 100\n",
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"second = round(n * 0.6)\n",
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"third = round(n * 0.4)\n",
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"\n",
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"year = np.array(['Second'] * second + ['Third'] * third)\n",
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"major = np.array(['Declared'] * (round(second * 0.5)) + ['Undeclared'] * (round(second * 0.5)) + \\\n",
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" ['Declared'] * (round(third * 0.8)) + ['Undeclared'] * (round(third * 0.2)))\n",
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" \n",
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"students = Table().with_columns(\n",
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" 'Year', year,\n",
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" 'Major', major\n",
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")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"def create_population(prior_disease_prob, n):\n",
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" disease = round(n * prior_disease_prob)\n",
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" no_disease = round(n * (1 - prior_disease_prob))\n",
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"\n",
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" status = np.array(['Disease'] * disease + ['No disease'] * no_disease)\n",
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" result = np.array(['Test +'] * (disease) + ['Test +'] * (round(no_disease * 0.05)) + \\\n",
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" ['Test -'] * (round(no_disease * 0.95)))\n",
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" \n",
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" t = Table().with_columns(\n",
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" 'Status', status,\n",
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" 'Test Result', result\n",
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" )\n",
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" return t.pivot('Test Result', 'Status')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## More Likely Than Not ##"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"students.show(3)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"students.pivot('Major', 'Year')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Verify: 60% of students are Second years, 40% are Third years\n",
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"60 / (60 + 40)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Verify: 50% of Second years have Declared\n",
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"30 / 60"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Verify: 80% of Third years have Declared\n",
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"32 / 40"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Chance of second year, given that they have declared\n",
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"# P(second year | declared)\n",
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"\n",
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"30 / 62"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# P(third year | declared)\n",
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"\n",
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"32 / 62"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Tree Diagram Calculation"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# P(second year | declared), from tree diagram\n",
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"\n",
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"(0.6 * 0.5) / (0.6 * 0.5 + 0.4 * 0.8)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Decisions ##"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"create_population(1/1000, 10000)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"10 / 510"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# P(disease | tested +)\n",
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"\n",
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"# = P(disease & tested +) / P(tested +)\n",
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"\n",
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"# if prior probability of disease is 1/10\n",
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"\n",
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"(0.1 * 1) / (0.1*1 + 0.9*0.05)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"create_population(1/10, 10000)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# P(disease | tested +)\n",
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"# if prior probability of disease is 0.5\n",
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"\n",
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"(0.5 * 1) / (0.5*1 + 0.5*0.05)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"create_population(1/2, 10000)"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.5"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}

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