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Lecture 04: Building Models

Objective Discuss practical considerations in model building

Reading Jensen and Nielsen, Chapter 3

Outline Catching the structure Determining probabilities Reducing the number of parameters Other Issues

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Catching the Structure

Identify the variables

Hypothesis variables Those whose values are not directly observed, and we wish to estimate

Information variables Those whose values are observed directly observed and contain information

about the hypothesis variables

Mediating variables Those that provide information channels between the information variables and

the hypothesis variables

Build the structure

Begin with causality

Consider conditional independence

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Example: Sore ThroatPage 3

Angina is chest pain or discomfort that occurs when an area of your heart muscle doesn't get enough oxygen-rich blood.

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Example: Sore Throat

Check conditional independence

Fever independent of Spots given Angina?

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Example: Infected MilkPage 5

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Example: Infected MilkPage 6

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Example: Infected MilkPage 7

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Example: Insemination of a cowPage 8

Insemination is the process of impregnating the femalemale

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Example: Insemination of a cowPage 9

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Why Mediating VariablesPage 10

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Example: Simplified Poker GamePage 11

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Example: Simplified Poker GamePage 12

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P(OH0), P(FC|OH0), P(OH1|OH0, FC), P(SC|OH1), P(OH|OH1, SC) are easier to obtain than P(OH|FC, SC)

Will see later

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SummaryPage 14

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Outline

Outline Catching the structure Determining probabilities Reducing the number of parameters Other Issues

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P(Test|Inf) from Sensitivity & Specificity of Test

P( Test=y | Inf=y ) = sensitivity

P( Test=y| inf=n) = 1-specificity

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Stud Farm Inference Results

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Outline

Outline Catching the structure Determining probabilities Reducing the number of parameters Other Issues

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Outline

Outline Catching the structure Determining probabilities Reducing the number of parameters Other issues

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Logical Constraints

Sometimes relationships among variables are undirected

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Logical ConstraintsPage 41

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Probabilities need not be exact to be useful

Some people have shied away from using Bayes nets because they imagine

they will only work well, if the probabilities upon which they are based are

exact.

This is not true. It turns out very often that approximate probabilities, even

subjective ones that are guessed at, give very good results. Bayes nets are

generally quite robust to imperfect knowledge.

Often the combination of several strands of imperfect knowledge can allow us

to make surprisingly strong conclusions.

In some cases, we have no choice but trust judgments by experts

If we can trust decisions by experts, then we can trust the probability

assessments by experts

Bayes nets can help experts make better decisions, albeit subjective.

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Causal Conditional Probabilities are easier to estimate than the reverse

Studies have shown people are better at estimating probabilities "in

the forward direction".

For example, doctors are quite good at giving the probability

estimates for "if the patient has lung cancer, what are the chances

their X-ray will be abnormal?",

rather than the reverse, "if the X-ray is abnormal, what are the

chances of lung cancer being the cause?" (Jensen96)

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