Risk Assessment and Decision Analysis with Bayesian Networks

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Contents

Foreword .......................................................................................................................................................xi

Preface........................................................................................................................................................ xiii

Acknowledgments ...................................................................................................................................... xvii

Authors ........................................................................................................................................................ xix

Chapter 1 There Is More to Assessing Risk Than Statistics ...................................................................1

1.1 Introduction ..................................................................................................................1

1.2 Predicting Economic Growth: The Normal Distribution and Its Limitations .............3

1.3 Patterns and Randomness: From School League Tables to Siegfried and Roy ...........7

1.4 Dubious Relationships: Why You Should Be Very Wary of Correlations and

Their Signicance Values .......................................................................................... 10

1.5 Spurious Correlations: How You Can Always Find a Silly ‘Cause’ of Exam

Success ....................................................................................................................... 14

1.6 The Danger of Regression: Looking Back When You Need to Look Forward ......... 16

1.7 The Danger of Averages ............................................................................................. 18

1.7.1 What Type of Average? ................................................................................. 19

1.7.2 When Averages Alone Will Never Be Sufcient for Decision Making ........20

1.8 When Simpson’s Paradox Becomes More Worrisome ............................................... 21

1.9 Uncertain Information and Incomplete Information: Do Not Assume They Are

Different .....................................................................................................................23

1.10 Do Not Trust Anybody (Even Experts) to Properly Reason about Probabilities .......26

1.11 Chapter Summary ......................................................................................................29

Further Reading ....................................................................................................................29

Chapter 2 The Need for Causal, Explanatory Models in Risk Assessment .......................................... 31

2.1 Introduction ................................................................................................................ 31

2.2 Are You More Likely to Die in an Automobile Crash When the Weather Is

Good Compared to Bad? ............................................................................................ 31

2.3 When Ideology and Causation Collide .......................................................................35

2.4 The Limitations of Common Approaches to Risk Assessment .................................37

2.4.1 Measuring Armageddon and Other Risks ....................................................37

2.4.2 Risks and Opportunities................................................................................39

2.4.3 Risk Registers and Heat Maps ......................................................................40

2.5 Thinking about Risk Using Causal Analysis ............................................................. 42

2.6 Applying the CausalFramework to Armageddon ......................................................46

2.7 Summary .................................................................................................................... 49

Further Reading ....................................................................................................................49

Chapter 3 Measuring Uncertainty: The Inevitability of Subjectivity .................................................... 51

3.1 Introduction ................................................................................................................ 51

3.2 Experiments, Outcomes, and Events .......................................................................... 52

3.2.1 Multiple Experiments ....................................................................................56

3.2.2 Joint Experiments .......................................................................................... 57

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3.2.3 Joint Events and Marginalization ..................................................................58

3.3 Frequentist versus Subjective View of Uncertainty ...................................................60

3.4 Summary .................................................................................................................... 67

Further Reading .....................................................................................................................68

Chapter 4 The Basics of Probability ...................................................................................................... 69

4.1 Introduction ................................................................................................................69

4.2 Some Observations Leading to Axioms and Theorems of Probability .....................69

4.3 Probability Distributions ............................................................................................ 81

4.3.1 Probability Distributions with Innite Outcomes .........................................83

4.3.2 Joint Probability Distributions and Probability of Marginalized Events ......85

4.3.3 Dealing with More than Two Variables ........................................................ 88

4.4 Independent Events and Conditional Probability .......................................................89

4.5 Binomial Distribution .................................................................................................96

4.6 Using Simple Probability Theory to Solve Earlier Problems and Explain

Widespread Misunderstandings ............................................................................... 101

4.6.1 The Birthday Problem ................................................................................. 101

4.6.2 The Monty Hall Problem ............................................................................103

4.6.3 When Incredible Events Are Really Mundane ........................................... 105

4.6.4 When Mundane Events Really Are Quite Incredible ................................. 109

4.7 Summary .................................................................................................................. 110

Further Reading .................................................................................................................. 111

Chapter 5 Bayes’ Theorem and Conditional Probability ..................................................................... 113

5.1 Introduction .............................................................................................................. 113

5.2 All Probabilities Are Conditional ............................................................................ 113

5.3 Bayes’ Theorem ........................................................................................................ 116

5.4 Using Bayes’ Theorem to Debunk Some Probability Fallacies ............................... 121

5.4.1 Traditional Statistical Hypothesis Testing ..................................................122

5.4.2 The Prosecutor Fallacy Revisited ...............................................................124

5.4.3 The Defendant’s Fallacy .............................................................................124

5.4.4 Odds Form of Bayes and the Likelihood Ratio ..........................................125

5.5 Second-Order Probability ........................................................................................ 127

5.6 Summary .................................................................................................................. 129

Further Reading .................................................................................................................. 129

Chapter 6 From Bayes’ Theorem to Bayesian Networks ..................................................................... 131

6.1 Introduction .............................................................................................................. 131

6.2 A Very Simple Risk Assessment Problem ............................................................... 132

6.3 Accounting for Multiple Causes (and Effects) .........................................................134

6.4 Using Propagation to Make Special Types of Reasoning Possible ..........................137

6.5 The Crucial Independence Assumptions ................................................................. 139

6.6 Structural Properties of BNs .................................................................................... 144

6.6.1 Serial Connection: Causal and Evidential Trails ........................................ 144

6.6.2 Diverging Connection: Common Cause ..................................................... 147

6.6.3 Converging Connection: Common Effect ................................................... 149

6.6.4 Determining Whether Any Two Nodes in a BN Are Dependent ............... 151