{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Think Bayes\n", "\n", "This notebook presents code and exercises from Think Bayes, second edition.\n", "\n", "Copyright 2018 Allen B. Downey\n", "\n", "MIT License: https://opensource.org/licenses/MIT" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Configure Jupyter so figures appear in the notebook\n", "%matplotlib inline\n", "\n", "# Configure Jupyter to display the assigned value after an assignment\n", "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n", "\n", "import math\n", "import numpy as np\n", "\n", "from thinkbayes2 import Pmf, Cdf, Suite, Joint\n", "import thinkplot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The flea beetle problem\n", "\n", "Different species of flea beetle can be distinguished by the width and angle of the aedeagus. The data below includes measurements and know species classification for 74 specimens.\n", "\n", "Suppose you discover a new specimen under conditions where it is equally likely to be any of the three species. You measure the aedeagus and width 140 microns and angle 15 (in multiples of 7.5 degrees). What is the probability that it belongs to each species?\n", "\n", "This problem is based on [this data story on DASL](https://web.archive.org/web/20160304083805/http://lib.stat.cmu.edu/DASL/Datafiles/FleaBeetles.html)\n", "\n", "Datafile Name: Flea Beetles\n", "\n", "Datafile Subjects: Biology\n", "\n", "Story Names: Flea Beetles\n", "\n", "Reference: Lubischew, A.A. (1962) On the use of discriminant functions in taxonomy. Biometrics, 18, 455-477. Also found in: Hand, D.J., et al. (1994) A Handbook of Small Data Sets, London: Chapman & Hall, 254-255.\n", "\n", "Authorization: Contact Authors\n", "\n", "Description: Data were collected on the genus of flea beetle Chaetocnema, which contains three species: concinna (Con), heikertingeri (Hei), and heptapotamica (Hep). Measurements were made on the width and angle of the aedeagus of each beetle. The goal of the original study was to form a classification rule to distinguish the three species.\n", "\n", "Number of cases: 74\n", "\n", "Variable Names:\n", "\n", "Width: The maximal width of aedeagus in the forpart (in microns)\n", "\n", "Angle: The front angle of the aedeagus (1 unit = 7.5 degrees)\n", "\n", "Species: Species of flea beetle from the genus Chaetocnema\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To solve this problem we have to account for two sources of uncertainty: given the data, we have some uncertainty about the actual distribution of attributes. Then, given the measurements, we have uncertainty about which species we have.\n", "\n", "First I'll load the data." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(140, 15)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "measurements = (140, 15)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", " | Width | \n", "Angle | \n", "Species | \n", "
---|---|---|---|
0 | \n", "150 | \n", "15 | \n", "Con | \n", "
1 | \n", "147 | \n", "13 | \n", "Con | \n", "
2 | \n", "144 | \n", "14 | \n", "Con | \n", "
3 | \n", "144 | \n", "16 | \n", "Con | \n", "
4 | \n", "153 | \n", "13 | \n", "Con | \n", "