Content: There Is More to Assessing Risk Than Statistics Introduction Predicting Economic Growth: The Normal Distribution and Its Limitations Patterns and Randomness: From School League Tables to Siegfried and Roy Dubious Relationships: Why You Should Be Very Wary of Correlations and Their Significance Values Spurious Correlations: How You Can Always Find a Silly 'Cause' of Exam Success The Danger of Regression: Looking Back When You Need to Look Forward The Danger of Averages When Simpson's Paradox Becomes More Worrisome Uncertain Information and Incomplete Information: Do Not Assume They Are Different Do Not Trust Anybody (Even Experts) to Properly Reason about Probabilities Chapter Summary Further Reading The Need for Causal, Explanatory Models in Risk Assessment Introduction Are You More Likely to Die in an Automobile Crash When the Weather Is Good Compared to Bad? The Limitations of Common Approaches to Risk Assessment Thinking about Risk Using Causal Analysis Applying the Causal Framework to Armageddon Summary Further Reading Measuring Uncertainty: The Inevitability of Subjectivity Introduction Experiments, Outcomes, and Events Frequentist versus Subjective View of Uncertainty Summary Further Reading The Basics of Probability Introduction Some Observations Leading to Axioms and Theorems of Probability Probability Distributions Independent Events and Conditional Probability Binomial Distribution Using Simple Probability Theory to Solve Earlier Problems and Explain Widespread Misunderstandings Summary Further Reading Bayes' Theorem and Conditional Probability Introduction All Probabilities Are Conditional Bayes' Theorem Using Bayes' Theorem to Debunk Some Probability Fallacies Second-Order Probability Summary Further Reading From Bayes' Theorem to Bayesian Networks Introduction A Very Simple Risk Assessment Problem Accounting for Multiple Causes (and Effects) Using Propagation to Make Special Types of Reasoning Possible The Crucial Independence Assumptions Structural Properties of BNs Propagation in Bayesian Networks Using BNs to Explain Apparent Paradoxes Steps in Building and Running a BN Model Summary Further Reading Theoretical Underpinnings BN Applications Nature and Theory of Causality Uncertain Evidence (Soft and Virtual) Defining the Structure of Bayesian Networks Introduction Causal Inference and Choosing the Correct Edge Direction The Idioms The Problems of Asymmetry and How to Tackle Them Multiobject Bayesian Network Models The Missing Variable Fallacy Conclusions Further Reading Building and Eliciting Node Probability Tables Introduction Factorial Growth in the Size of Probability Tables Labeled Nodes and Comparative Expressions Boolean Nodes and Functions Ranked Nodes Elicitation Summary Further Reading Numeric Variables and Continuous Distribution Functions Introduction Some Theory on Functions and Continuous Distributions Static Discretization Dynamic Discretization Using Dynamic Discretization Avoiding Common Problems When Using Numeric Nodes Summary Further Reading Hypothesis Testing and Confidence Intervals Introduction Hypothesis Testing Confidence Intervals Summary Further Reading Modeling Operational Risk Introduction The Swiss Cheese Model for Rare Catastrophic Events Bow Ties and Hazards Fault Tree Analysis (FTA) Event Tree Analysis (ETA) Soft Systems, Causal Models, and Risk Arguments KUUUB Factors Operational Risk in Finance Summary Further Reading Systems Reliability Modeling Introduction Probability of Failure on Demand for Discrete Use Systems Time to Failure for Continuous Use Systems System Failure Diagnosis and Dynamic Bayesian Networks Dynamic Fault Trees (DFTs) Software Defect Prediction Summary Further Reading Bayes and the Law Introduction The Case for Bayesian Reasoning about Legal Evidence Building Legal Arguments Using Idioms The Evidence Idiom The Evidence Accuracy Idiom Idioms to Deal with the Key Notions of "Motive" and "Opportunity" Idiom for Modeling Dependency between Different Pieces of Evidence Alibi Evidence Idiom Putting it All Together: Vole Example Using BNs to Expose Further Fallacies of Legal Reasoning Summary Further Reading Appendix A: The Basics of Counting Appendix B: The Algebra of Node Probability Tables Appendix C: Junction Tree Algorithm Appendix D: Dynamic Discretization Appendix E: Statistical Distributions