Foreword |
|
xv | |
Preface |
|
xvii | |
Acknowledgments |
|
xix | |
Authors |
|
xxi | |
Chapter 1 Introduction |
|
1 | (8) |
Chapter 2 Debunking Bad Statistics |
|
9 | (36) |
|
2.1 Predicting Economic Growth: The Normal Distribution and Its Limitations |
|
|
9 | (5) |
|
2.2 Patterns and Randomness: From School League Tables to Siegfried and Roy |
|
|
14 | (3) |
|
2.3 Dubious Relationships: Why You Should Be Very Wary of Correlations and Their Significance Values |
|
|
17 | (5) |
|
2.4 Spurious Correlations: How You Can Always Find a Silly "Cause" of Exam Success |
|
|
22 | (1) |
|
2.5 The Danger of Regression: Looking Back When You Need to Look Forward |
|
|
23 | (3) |
|
2.6 The Danger of Averages |
|
|
26 | (3) |
|
2.6.1 What Type of Average? |
|
|
27 | (1) |
|
2.6.2 When Averages Alone Will Never Be Sufficient for Decision Making |
|
|
28 | (1) |
|
2.7 When Simpson's Paradox Becomes More Worrisome |
|
|
29 | (1) |
|
2.8 How We Measure Risk Can Dramatically Change Our Perception of Risk |
|
|
30 | (4) |
|
2.9 Why Relying on Data Alone Is Insufficient for Risk Assessment |
|
|
34 | (2) |
|
2.10 Uncertain Information and Incomplete Information: Do Not Assume They Are Different |
|
|
36 | (3) |
|
2.11 Do Not Trust Anybody (Even Experts) to Properly Reason about Probabilities |
|
|
39 | (3) |
|
|
42 | (1) |
|
|
42 | (3) |
Chapter 3 The Need for Causal, Explanatory Models in Risk Assessment |
|
45 | (22) |
|
|
45 | (1) |
|
3.2 Are You More Likely to Die in an Automobile Crash When the Weather Is Good Compared to Bad? |
|
|
45 | (4) |
|
3.3 When Ideology and Causation Collide |
|
|
49 | (2) |
|
3.4 The Limitations of Common Approaches to Risk Assessment |
|
|
51 | (5) |
|
3.4.1 Measuring Armageddon and Other Risks |
|
|
51 | (2) |
|
3.4.2 Risks and Opportunities |
|
|
53 | (1) |
|
3.4.3 Risk Registers and Heat Maps |
|
|
54 | (2) |
|
3.5 Thinking about Risk Using Causal Analysis |
|
|
56 | (4) |
|
3.6 Applying the Causal Framework to Armageddon |
|
|
60 | (3) |
|
3.7 Decisions and Utilities |
|
|
63 | (1) |
|
|
64 | (1) |
|
|
65 | (2) |
Chapter 4 Measuring Uncertainty: The Inevitability of Subjectivity |
|
67 | (20) |
|
|
67 | (2) |
|
4.2 Experiments, Outcomes, and Events |
|
|
69 | (8) |
|
4.2.1 Multiple Experiments |
|
|
73 | (1) |
|
|
74 | (1) |
|
4.2.3 Joint Events and Marginalization |
|
|
75 | (2) |
|
4.3 Frequentist versus Subjective View of Uncertainty |
|
|
77 | (7) |
|
|
84 | (1) |
|
|
85 | (2) |
Chapter 5 The Basics of Probability |
|
87 | (44) |
|
|
87 | (1) |
|
5.2 Some Observations Leading to Axioms and Theorems of Probability |
|
|
87 | (12) |
|
5.3 Probability Distributions |
|
|
99 | (8) |
|
5.3.1 Probability Distributions with Infinite Outcomes |
|
|
101 | (2) |
|
5.3.2 Joint Probability Distributions and Probability of Marginalized Events |
|
|
103 | (3) |
|
5.3.3 Dealing with More than Two Variables |
|
|
106 | (1) |
|
5.4 Independent Events and Conditional Probability |
|
|
107 | (7) |
|
5.5 Binomial Distribution |
|
|
114 | (5) |
|
5.6 Using Simple Probability Theory to Solve Earlier Problems and Explain Widespread Misunderstandings |
|
|
119 | (9) |
|
5.6.1 The Birthday Problem |
|
|
119 | (2) |
|
5.6.2 The Monty Hall Problem |
|
|
121 | (2) |
|
5.6.3 When Incredible Events Are Really Mundane |
|
|
123 | (4) |
|
5.6.4 When Mundane Events Really Are Quite Incredible |
|
|
127 | (1) |
|
|
128 | (1) |
|
|
129 | (2) |
Chapter 6 Bayes' Theorem and Conditional Probability |
|
131 | (24) |
|
|
131 | (1) |
|
6.2 All Probabilities Are Conditional |
|
|
131 | (3) |
|
|
134 | (5) |
|
6.4 Using Bayes' Theorem to Debunk Some Probability Fallacies |
|
|
139 | (5) |
|
6.4.1 Traditional Statistical Hypothesis Testing |
|
|
140 | (2) |
|
6.4.2 The Prosecutor Fallacy Revisited |
|
|
142 | (1) |
|
6.4.3 The Defendant's Fallacy |
|
|
142 | (1) |
|
6.4.4 Odds Form of Bayes and the Likelihood Ratio |
|
|
143 | (1) |
|
6.5 Likelihood Ratio as a Measure of Probative Value of Evidence: Benefits and Dangers |
|
|
144 | (8) |
|
6.5.1 The (Only) Natural Definition of Probative Value of Evidence |
|
|
145 | (1) |
|
6.5.2 A Measure of Probative Value of Evidence |
|
|
146 | (2) |
|
6.5.3 Problem with the LR |
|
|
148 | (3) |
|
6.5.4 Calculating the LR When We Know P(HIE) Rather Than P(EIH) |
|
|
151 | (1) |
|
6.6 Second-Order Probability |
|
|
152 | (2) |
|
|
154 | (1) |
|
|
154 | (1) |
Chapter 7 From Bayes' Theorem to Bayesian Networks |
|
155 | (46) |
|
|
155 | (1) |
|
7.2 A Very Simple Risk Assessment Problem |
|
|
156 | (2) |
|
7.3 Accounting for Multiple Causes (and Effects) |
|
|
158 | (3) |
|
7.4 Using Propagation to Make Special Types of Reasoning Possible |
|
|
161 | (2) |
|
7.5 The Crucial Independence Assumptions |
|
|
163 | (5) |
|
7.6 Structural Properties of BNs |
|
|
168 | (9) |
|
7.6.1 Serial Connection: Causal and Evidential Trails |
|
|
168 | (3) |
|
7.6.2 Diverging Connection: Common Cause |
|
|
171 | (2) |
|
7.6.3 Converging Connection: Common Effect |
|
|
173 | (2) |
|
7.6.4 Determining Whether Any Two Nodes in a BN Are Dependent |
|
|
175 | (2) |
|
7.7 Propagation in Bayesian Networks |
|
|
177 | (3) |
|
7.8 Steps in Building and Running a BN Model |
|
|
180 | (5) |
|
7.8.1 Building a BN Model |
|
|
180 | (3) |
|
|
183 | (1) |
|
7.8.3 Inconsistent Evidence |
|
|
184 | (1) |
|
7.9 Using BNs to Explain Apparent Paradoxes |
|
|
185 | (9) |
|
7.9.1 Revisiting the Monty Hall Problem |
|
|
185 | (5) |
|
|
185 | (1) |
|
|
185 | (5) |
|
7.9.2 Revisiting Simpson's Paradox |
|
|
190 | (3) |
|
7.9.3 Refuting the Assertion "If There Is No Correlation Then There Cannot be Causation" |
|
|
193 | (1) |
|
7.10 Modelling Interventions and Counterfactual Reasoning in BNs |
|
|
194 | (3) |
|
|
194 | (1) |
|
|
195 | (2) |
|
|
197 | (1) |
|
|
198 | (3) |
Chapter 8 Defining the Structure of Bayesian Networks |
|
201 | (46) |
|
|
201 | (1) |
|
8.2 Causal Inference and Choosing the Correct Edge Direction |
|
|
202 | (2) |
|
|
204 | (16) |
|
8.3.1 The Cause-Consequence Idiom |
|
|
205 | (2) |
|
|
207 | (7) |
|
8.3.3 Definitional/Synthesis Idiom |
|
|
214 | (5) |
|
8.3.3.1 Case 1: Definitional Relationship between Variables |
|
|
214 | (1) |
|
8.3.3.2 Case 2: Hierarchical Definitions |
|
|
215 | (1) |
|
8.3.3.3 Case 3: Combining Different Nodes Together to Reduce Effects of Combinatorial Explosion ("Divorcing") |
|
|
216 | (3) |
|
|
219 | (1) |
|
8.4 The Problems of Asymmetry and How to Tackle Them |
|
|
220 | (13) |
|
|
221 | (2) |
|
8.4.2 Mutually Exclusive Paths |
|
|
223 | (2) |
|
8.4.3 Mutually Exclusive Events and Pathways |
|
|
225 | (3) |
|
8.4.4 Taxonomic Classification |
|
|
228 | (5) |
|
8.5 Multiobject Bayesian Network Models |
|
|
233 | (7) |
|
8.6 The Missing Variable Fallacy |
|
|
240 | (4) |
|
|
244 | (1) |
|
|
245 | (2) |
Chapter 9 Building and Eliciting Node Probability Tables |
|
247 | (52) |
|
|
247 | (1) |
|
9.2 Factorial Growth in the Size of Probability Tables |
|
|
247 | (2) |
|
9.3 Labeled Nodes and Comparative Expressions |
|
|
249 | (4) |
|
9.4 Boolean Nodes and Functions |
|
|
253 | (22) |
|
|
254 | (3) |
|
9.4.2 The OR Function for Boolean Nodes |
|
|
257 | (5) |
|
9.4.3 The AND Function for Boolean Nodes |
|
|
262 | (3) |
|
|
265 | (1) |
|
9.4.5 NoisyOR Function for Boolean Nodes |
|
|
265 | (6) |
|
9.4.6 NoisyAND Function for Boolean Nodes |
|
|
271 | (2) |
|
|
273 | (2) |
|
|
275 | (17) |
|
|
275 | (2) |
|
9.5.2 Solution: Ranked Nodes with the TNormal Distribution |
|
|
277 | (6) |
|
9.5.3 Alternative Weighted Functions for Ranked Nodes When Weighted Mean Is Insufficient |
|
|
283 | (3) |
|
9.5.4 Hints and Tips When Working with Ranked Nodes and NPTs |
|
|
286 | (6) |
|
9.5.4.1 Tip 1: Use the Weighted Functions as Far as Possible |
|
|
286 | (1) |
|
9.5.4.2 Tip 2: Exploit the Fact That a Ranked Node Parent Has an Underlying Numerical Scale |
|
|
286 | (1) |
|
9.5.4.3 Tip 3: Do Not Forget the Importance of the Variance in the TNormal Distribution |
|
|
287 | (4) |
|
9.5.4.4 Tip 4: Change the Granularity of a Ranked Scale without Having to Make Any Other Changes |
|
|
291 | (1) |
|
9.5.4.5 Tip 5: Do Not Create Large, Deep, Hierarchies Consisting of Rank Nodes |
|
|
292 | (1) |
|
|
292 | (4) |
|
9.6.1 Elicitation Protocols and Cognitive Biases |
|
|
292 | (3) |
|
9.6.2 Validation and Scoring Rules |
|
|
295 | (1) |
|
|
296 | (1) |
|
|
297 | (2) |
Chapter 10 Numeric Variables and Continuous Distribution Functions |
|
299 | (48) |
|
|
299 | (1) |
|
10.2 Some Theory on Functions and Continuous Distributions |
|
|
300 | (5) |
|
10.3 Static Discretization |
|
|
305 | (7) |
|
10.4 Dynamic Discretization |
|
|
312 | (4) |
|
10.5 Using Dynamic Discretization |
|
|
316 | (17) |
|
10.5.1 Prediction Using Dynamic Discretization |
|
|
316 | (3) |
|
10.5.2 Conditioning on Discrete Evidence |
|
|
319 | (3) |
|
10.5.3 Parameter Learning (Induction) Using Dynamic Discretization |
|
|
322 | (11) |
|
10.5.3.1 Classical versus Bayesian Modeling |
|
|
322 | (5) |
|
10.5.3.2 Bayesian Hierarchical Model Using Beta-Binomial |
|
|
327 | (6) |
|
10.6 Risk Aggregation, Compound Sum Analysis and the Loss Distribution Approach |
|
|
333 | (7) |
|
10.6.1 Aggregating Distributions |
|
|
333 | (1) |
|
10.6.2 Calculating a Loss Distribution and Using the Compound Sum Analysis Tool |
|
|
334 | (6) |
|
10.7 Tips and Tricks when Using Numeric Nodes |
|
|
340 | (4) |
|
10.7.1 Unintentional Negative Values in a Node's State Range |
|
|
340 | (2) |
|
10.7.2 Faster Approximation When Doing Prediction |
|
|
342 | (1) |
|
10.7.3 Observations with Very Low Probability |
|
|
343 | (1) |
|
10.7.4 "Tail Discretisation" |
|
|
343 | (1) |
|
|
344 | (1) |
|
|
345 | (2) |
Chapter 11 Decision Analysis, Decision Trees, Value of Information Analysis, and Sensitivity Analysis |
|
347 | (24) |
|
|
347 | (2) |
|
11.2 Hybrid Influence Diagrams |
|
|
349 | (3) |
|
|
352 | (2) |
|
11.4 Advanced Hybrid Influence Diagrams |
|
|
354 | (7) |
|
11.5 Value of Information Analysis |
|
|
361 | (5) |
|
11.6 Sensitivity Analysis |
|
|
366 | (2) |
|
|
368 | (1) |
|
|
369 | (2) |
Chapter 12 Hypothesis Testing and Confidence Intervals |
|
371 | (54) |
|
|
371 | (1) |
|
12.2 The Fundamentals of Hypothesis Testing |
|
|
371 | (11) |
|
12.2.1 Using p-Values and the Classical Approach |
|
|
372 | (4) |
|
12.2.2 The Bayesian Approach Avoids p-Values Completely |
|
|
376 | (6) |
|
12.3 Testing for Hypothetical Differences |
|
|
382 | (13) |
|
12.3.1 General Approach to Testing Differences between Attributes |
|
|
382 | (5) |
|
12.3.2 Considering Difference between Distributions Rather Than Difference between Means |
|
|
387 | (5) |
|
12.3.3 Bayesian Network Solution to the Problem of Learning Population Mean and Variance from Sample Mean and Variance |
|
|
392 | (3) |
|
12.3.4 Summary of the Issues Raised Comparing Classical Statistical Hypothesis Testing and the Bayesian Approach |
|
|
395 | (1) |
|
12.4 Bayes Factors and Model Comparison |
|
|
395 | (21) |
|
|
396 | (2) |
|
12.4.2 Model Comparison: Choosing the Best Predictive Model |
|
|
398 | (6) |
|
12.4.3 Accommodating Expert Judgments about Hypotheses |
|
|
404 | (3) |
|
12.4.4 Distribution Fitting as Hypothesis Testing |
|
|
407 | (1) |
|
12.4.5 Bayesian Model Comparison and Complex Causal Hypotheses |
|
|
408 | (8) |
|
12.5 Confidence Intervals |
|
|
416 | (6) |
|
12.5.1 The Fallacy of Frequentist Confidence Intervals |
|
|
416 | (3) |
|
12.5.2 The Bayesian Alternative to Confidence Intervals |
|
|
419 | (3) |
|
|
422 | (1) |
|
|
423 | (2) |
Chapter 13 Modeling Operational Risk |
|
425 | (38) |
|
|
425 | (1) |
|
13.2 The Swiss Cheese Model for Rare Catastrophic Events |
|
|
426 | (3) |
|
13.3 Bow Ties and Hazards |
|
|
429 | (1) |
|
13.4 Fault Tree Analysis (FTA) |
|
|
430 | (6) |
|
13.5 Event Tree Analysis (ETA) |
|
|
436 | (3) |
|
13.6 Soft Systems, Causal Models, and Risk Arguments |
|
|
439 | (5) |
|
|
444 | (2) |
|
13.8 Operational Risk in Finance |
|
|
446 | (12) |
|
13.8.1 Modeling the Operational Loss Generation Process |
|
|
447 | (7) |
|
13.8.2 Scenarios and Stress Testing |
|
|
454 | (4) |
|
13.9 Cyber Security Risk Modelling |
|
|
458 | (2) |
|
|
460 | (1) |
|
|
461 | (2) |
Chapter 14 Systems Reliability Modeling |
|
463 | (30) |
|
|
463 | (1) |
|
14.2 Probability of Failure on Demand for Discrete Use Systems |
|
|
464 | (4) |
|
14.3 Time to Failure for Continuous Use Systems |
|
|
468 | (3) |
|
14.4 System Failure Diagnosis and Dynamic Bayesian Networks |
|
|
471 | (4) |
|
14.5 Dynamic Fault Trees (DFTs) |
|
|
475 | (9) |
|
14.6 Software Defect Prediction |
|
|
484 | (7) |
|
|
491 | (1) |
|
|
492 | (1) |
Chapter 15 The Role of Bayes in Forensic and Legal Evidence Presentation |
|
493 | (30) |
|
|
493 | (1) |
|
15.2 Context and Review of Bayes in Legal Proceedings |
|
|
494 | (5) |
|
15.3 Basics of Bayes for Reasoning about Legal Evidence |
|
|
499 | (6) |
|
15.4 The Problems with Trying to Avoid Using Prior Probabilities with the Likelihood Ratio |
|
|
505 | (2) |
|
15.5 Computing the Likelihood Ratio in Practice: When It Is Easy and When It Requires Full BN Inference |
|
|
507 | (6) |
|
15.6 Practical Limitations of the Use of the Likelihood Ratio in Legal Reasoning |
|
|
513 | (7) |
|
15.6.1 Exhaustiveness and Mutual Exclusivity of Hypotheses Is Not Always Possible in Practical Likelihood Ratio Uses |
|
|
514 | (4) |
|
15.6.2 The Likelihood Ratio for Source-Level Hypotheses May Tell Us Nothing about Activity and Offense-Level Hypotheses |
|
|
518 | (1) |
|
15.6.3 Confusion about Likelihood Ratio Being Expressed on a Verbal Scale |
|
|
519 | (1) |
|
|
520 | (1) |
|
|
520 | (3) |
Chapter 16 Building and Using Bayesian Networks for Legal Reasoning |
|
523 | (30) |
|
|
523 | (1) |
|
16.2 The Evidence Accuracy Idiom |
|
|
524 | (2) |
|
16.3 Idioms to Deal with the Key Notions of "Opportunity" and "Motive" |
|
|
526 | (5) |
|
|
527 | (3) |
|
|
530 | (1) |
|
16.4 Idiom for Modeling Dependency between Different Pieces of Evidence |
|
|
531 | (3) |
|
16.5 Alibi Evidence Idiom |
|
|
534 | (2) |
|
16.6 Explaining Away Idiom |
|
|
536 | (3) |
|
16.7 Putting It All Together: Vole Example |
|
|
539 | (4) |
|
16.8 Using Bayesian Networks to Expose Further Paradoxes and Fallacies of Legal Reasoning |
|
|
543 | (8) |
|
16.8.1 The Conjunction Paradox |
|
|
543 | (3) |
|
16.8.2 The Jury Observation Fallacy |
|
|
546 | (2) |
|
16.8.3 The Crimewatch UK Fallacy |
|
|
548 | (3) |
|
|
551 | (1) |
|
|
552 | (1) |
Chapter 17 Learning from Data in Bayesian Networks |
|
553 | (20) |
|
|
553 | (1) |
|
17.2 Learning Discrete Model Tables from Complete Data Sets |
|
|
554 | (2) |
|
17.3 Combing Expert Knowledge with Table Learning from Data |
|
|
556 | (1) |
|
17.4 Learning Table Values with Missing Data: Expectation Maximization for Discrete Models |
|
|
556 | (9) |
|
17.5 Expectation Maximization for Hybrid Models |
|
|
565 | (7) |
|
|
572 | (1) |
|
|
572 | (1) |
Appendix A: The Basics of Counting |
|
573 | (8) |
Appendix B: The Algebra of Node Probability Tables |
|
581 | (6) |
Appendix C: Junction Tree Algorithm |
|
587 | (10) |
Appendix D: Dynamic Discretization |
|
597 | (20) |
Appendix E: Statistical Distributions |
|
617 | (12) |
Index |
|
629 | |