Content: There Is More to Assessing Risk Than StatisticsIntroductionPredicting Economic Growth: The Normal Distribution and Its LimitationsPatterns and Randomness: From School League Tables to Siegfried and RoyDubious Relationships: Why You Should Be Very Wary of Correlations andTheir Significance ValuesSpurious Correlations: How You Can Always Find a Silly `Cause' of ExamSuccessThe Danger of Regression: Looking Back When You Need to Look ForwardThe Danger of AveragesWhen Simpson's Paradox Becomes More WorrisomeUncertain Information and Incomplete Information: Do Not Assume They AreDifferentDo Not Trust Anybody (Even Experts) to Properly Reason about ProbabilitiesChapter SummaryFurther ReadingThe Need for Causal, Explanatory Models in Risk AssessmentIntroductionAre You More Likely to Die in an Automobile Crash When the Weather IsGood Compared to Bad?The Limitations of Common Approaches to Risk AssessmentThinking about Risk Using Causal AnalysisApplying the Causal Framework to ArmageddonSummaryFurther ReadingMeasuring Uncertainty: The Inevitability of SubjectivityIntroductionExperiments, Outcomes, and EventsFrequentist versus Subjective View of UncertaintySummaryFurther ReadingThe Basics of ProbabilityIntroductionSome Observations Leading to Axioms and Theorems of ProbabilityProbability DistributionsIndependent Events and Conditional ProbabilityBinomial DistributionUsing Simple Probability Theory to Solve Earlier Problems and ExplainWidespread MisunderstandingsSummaryFurther ReadingBayes' Theorem and Conditional ProbabilityIntroductionAll Probabilities Are ConditionalBayes' Theorem Using Bayes' Theorem to Debunk Some Probability FallaciesSecond-Order ProbabilitySummaryFurther ReadingFrom Bayes' Theorem to Bayesian NetworksIntroductionA Very Simple Risk Assessment ProblemAccounting for Multiple Causes (and Effects)Using Propagation to Make Special Types of Reasoning PossibleThe Crucial Independence AssumptionsStructural Properties of BNsPropagation in Bayesian NetworksUsing BNs to Explain Apparent ParadoxesSteps in Building and Running a BN ModelSummaryFurther ReadingTheoretical UnderpinningsBN ApplicationsNature and Theory of CausalityUncertain Evidence (Soft and Virtual)Defining the Structure of Bayesian NetworksIntroductionCausal Inference and Choosing the Correct Edge DirectionThe IdiomsThe Problems of Asymmetry and How to Tackle ThemMultiobject Bayesian Network ModelsThe Missing Variable FallacyConclusionsFurther ReadingBuilding and Eliciting Node Probability TablesIntroductionFactorial Growth in the Size of Probability TablesLabeled Nodes and Comparative ExpressionsBoolean Nodes and FunctionsRanked NodesElicitationSummaryFurther ReadingNumeric Variables and Continuous Distribution FunctionsIntroductionSome Theory on Functions and Continuous DistributionsStatic DiscretizationDynamic DiscretizationUsing Dynamic DiscretizationAvoiding Common Problems When Using Numeric NodesSummaryFurther ReadingHypothesis Testing and Confidence IntervalsIntroductionHypothesis TestingConfidence IntervalsSummaryFurther ReadingModeling Operational RiskIntroductionThe Swiss Cheese Model for Rare Catastrophic EventsBow Ties and HazardsFault Tree Analysis (FTA)Event Tree Analysis (ETA)Soft Systems, Causal Models, and Risk ArgumentsKUUUB FactorsOperational Risk in FinanceSummaryFurther ReadingSystems Reliability ModelingIntroductionProbability of Failure on Demand for Discrete Use SystemsTime to Failure for Continuous Use SystemsSystem Failure Diagnosis and Dynamic Bayesian NetworksDynamic Fault Trees (DFTs)Software Defect PredictionSummaryFurther ReadingBayes and the LawIntroductionThe Case for Bayesian Reasoning about Legal EvidenceBuilding Legal Arguments Using IdiomsThe Evidence IdiomThe Evidence Accuracy IdiomIdioms to Deal with the Key Notions of "Motive" and "Opportunity"Idiom for Modeling Dependency between Different Pieces of EvidenceAlibi Evidence IdiomPutting it All Together: Vole ExampleUsing BNs to Expose Further Fallacies of Legal ReasoningSummaryFurther ReadingAppendix A: The Basics of CountingAppendix B: The Algebra of Node Probability TablesAppendix C: Junction Tree AlgorithmAppendix D: Dynamic DiscretizationAppendix E: Statistical Distributions