Lecture 04: Building Models

1. Page 1 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

2. Page 2 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

3. Page 3 Example: Sore Throat • Angina is chest pain or discomfort that occurs when an area of your heart muscle doesn't get enough oxygen-rich blood.

4. Page 4 Example: Sore Throat • Check conditional independence • Fever independent of Spots given Angina?

5. Page 5 Example: Infected Milk

6. Page 6 Example: Infected Milk

7. Page 7 Example: Infected Milk

8. Page 8 Example: Insemination of a cow • Insemination is the process of impregnating the femalemale

9. Page 9 Example: Insemination of a cow

10. Page 10 Why Mediating Variables

11. Page 11 Example: Simplified Poker Game

12. Page 12 Example: Simplified Poker Game

13. Page 13 • 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

14. Page 14 Summary

15. Page 15 Outline • Outline • Catching the structure • Determining probabilities • Reducing the number of parameters • Other Issues

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18. 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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25. Stud Farm Inference Results

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31. Page 31 Outline • Outline • Catching the structure • Determining probabilities • Reducing the number of parameters • Other Issues

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39. Page 39 Outline • Outline • Catching the structure • Determining probabilities • Reducing the number of parameters • Other issues

40. Sometimes relationships among variables are undirected Logical Constraints

41. Logical Constraints

44. 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.

45. 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)