The party animal. All the variables are binary. P = `been to party\', H = `got a

Question

The party animal. All the variables are binary.

P = `been to party', H = `got a headache', D = `demotivated at work', U = `underperform at work', and A = `boss is angry'. The shaded variables are observed in the true state.

The party animal problem corresponds to the network in Fig. 1. The boss is angry and the worker has a headache - what is the probability the worker has been to a party? To complete the specifications, the probabilities are given as follows:

p(U = tr | P = tr, D = tr) = 0.999 p(U = tr | P = fa, D = tr) = 0.9 p(H = tr | P = tr) = 0.9

p(U = tr | P = tr, D = fa) = 0.9 p(U = tr | P = fa, D = fa) = 0.01 p(H = tr | P = fa) = 0.2

p(A = tr| U = tr) = 0.95 p(A = tr | U = fa) = 0.5 p(P = tr) = 0.2 p(D = tr) = 0.4

Explanation / Answer

{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercises ", " ", "Disclaimer: the questions in the following solutions are not my own. ", "They are from [Bayesian Reasoning and Machine Learning](http://web4.cs.ucl.ac.uk/staff/D.Barber/textbook/091213.pdf) by David Barber. ", "These questions are available online there so it shouldn't be too much of an issue that I'm copying them out here. ", " ", "## 3.1 ", " ", "> The party animal problem corresponds to the network in fig(3.14). The boss ", "> is angry and the worker has a headache - what is the probability the worker has been to a party? To complete ", "> the specifications, the probabilities are given as follows: ", "> ", "> $$ \begin{matrix} p(U=tr|P=tr,D=tr) = 0.999 & p(U=tr|P=fa,D=tr) = 0.9 & p(H=tr|P=tr)=0.9 \\ ", " P(U=tr|P=tr,D=fa)=0.9 & p(U=tr|P=fa, D=fa) = 0.01 & p(H=tr|P=fa)=0.2 \\ ", " P(A=tr|U=tr)=0.95 & p(A=tr|U=fa)=0.5 & p(P=tr)=0.2, P(D=tr)=0.4 \end{matrix} $$ ", " ", "This corresponds to the belief network in figure 3.14. ", "What does that look like? ", "Will try to draw using [Daft](http://daft-pgm.org/)." ] },

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