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Table of Contents
Executive Summary; Acknowledgments; Contents; List of Figures; List of Tables; 1 Introduction; 1.1 Prologue; 1.2 Quintessential Bayes'; 1.3 Scope; 1.4 Motivation; 1.5 Intent; 1.6 Utility; 1.7 Introduction to Bayes' Theorem and Bayesian Belief Networks; 1.8 Inductive Versus Deductive Logic; 1.9 Popper's Logic of Scientific Discovery; 1.10 Frequentist Versus Bayesian (Subjective) Views; 1.10.1 Frequentist to Subjectivist Philosophy; 1.10.2 Bayesian Philosophy; 1.11 The Identification of the Truth; 1.12 Bayes' Theorem: An Introduction; 1.13 Classic Illustration-Monty Hall Game Show Paradox
1.13.1 Characteristics1.13.2 Assumptions; 1.13.3 Bayesian Belief Network Solution; Step 1: Specify the Joint BBN; Step 2: Calculate the Prior Probabilities; Step 3: Determine the Contestant and Car Likelihood Probabilities; Step 4: Determine the Host, Contestant, and Car Likelihood Probabilities; Step 5: Compute the Joint Probabilities; Step 6: Compute the Posterior Probabilities; 1.13.4 Conclusions; References; 2 Literature Review ; 2.1 Introduction to the Bayes' Theorem Evolution; 2.1.1 Early 1900s; 2.1.2 1920s-1930s; 2.1.3 1940s-1950s; 2.1.4 1960s-Mid 1980s; 2.1.5 Mid 1980s to Today
2.1.5.1 Financial Economics, Accounting, and Operational Risks2.1.5.2 Safety, Accident Analysis, and Prevention; 2.1.5.3 Engineering and Safety; 2.1.5.4 Risk Analysis; 2.1.5.5 Ecology; 2.1.5.6 Human Behavior; 2.1.5.7 Behavioral Sciences and Marketing; 2.1.5.8 Decision Support Systems (DSS) with Expert Systems (ES) and Applications, Information Sciences, Intelligent Data Analysis, Neuroimaging, Environmental Modeling and Software, and Industrial Ergonomics; 2.1.5.9 Cognitive Science; 2.1.5.10 Medical, Health, Dental, and Nursing; 2.1.5.11 Environmental Studies
2.1.5.12 Miscellaneous: Politics, Geriatrics, Space Policy, and Language and Speech2.1.5.13 Current Government and Commercial Users of Bayesian Belief Networks; 2.1.6 Trademarked Uses of Bayesian Belief Networks; References; 3 Statistical Properties of Bayes' Theorem; 3.1 Axioms of Probability; 3.2 Base-Rate Fallacy; 3.3 Bayes' Theorem; 3.3.1 Prior Probability; 3.3.2 Conditional Probability; 3.3.3 Joint and Marginal Probability; 3.3.4 Posterior Probability; 3.4 Joint and Disjoint Bayesian Belief Network Structures; 3.4.1 Joint BBN Structure
3.4.2 Disjoint (Pairwise) Bayesian Belief Network Structure3.5 Bayesian Updating; 3.5.1 Fully Specified Joint BBN; 3.5.2 Partially Specified Disjoint BBN; 3.6 Certain Event; 3.7 Categorical Variable; 3.8 Chain (Product) Rule; 3.9 Collectively Exhaustive; 3.10 Combinations and Permutations; 3.10.1 Combinations; 3.10.2 Permutations; 3.11 Complement and Complement Rule; 3.12 Conditional and Unconditional Probability; 3.12.1 Conditional Probability; 3.12.2 Unconditional Probability; 3.13 Counting and Countable Set and Uncountable Set; 3.13.1 Counting; 3.13.2 Countable and Countable Set
1.13.1 Characteristics1.13.2 Assumptions; 1.13.3 Bayesian Belief Network Solution; Step 1: Specify the Joint BBN; Step 2: Calculate the Prior Probabilities; Step 3: Determine the Contestant and Car Likelihood Probabilities; Step 4: Determine the Host, Contestant, and Car Likelihood Probabilities; Step 5: Compute the Joint Probabilities; Step 6: Compute the Posterior Probabilities; 1.13.4 Conclusions; References; 2 Literature Review ; 2.1 Introduction to the Bayes' Theorem Evolution; 2.1.1 Early 1900s; 2.1.2 1920s-1930s; 2.1.3 1940s-1950s; 2.1.4 1960s-Mid 1980s; 2.1.5 Mid 1980s to Today
2.1.5.1 Financial Economics, Accounting, and Operational Risks2.1.5.2 Safety, Accident Analysis, and Prevention; 2.1.5.3 Engineering and Safety; 2.1.5.4 Risk Analysis; 2.1.5.5 Ecology; 2.1.5.6 Human Behavior; 2.1.5.7 Behavioral Sciences and Marketing; 2.1.5.8 Decision Support Systems (DSS) with Expert Systems (ES) and Applications, Information Sciences, Intelligent Data Analysis, Neuroimaging, Environmental Modeling and Software, and Industrial Ergonomics; 2.1.5.9 Cognitive Science; 2.1.5.10 Medical, Health, Dental, and Nursing; 2.1.5.11 Environmental Studies
2.1.5.12 Miscellaneous: Politics, Geriatrics, Space Policy, and Language and Speech2.1.5.13 Current Government and Commercial Users of Bayesian Belief Networks; 2.1.6 Trademarked Uses of Bayesian Belief Networks; References; 3 Statistical Properties of Bayes' Theorem; 3.1 Axioms of Probability; 3.2 Base-Rate Fallacy; 3.3 Bayes' Theorem; 3.3.1 Prior Probability; 3.3.2 Conditional Probability; 3.3.3 Joint and Marginal Probability; 3.3.4 Posterior Probability; 3.4 Joint and Disjoint Bayesian Belief Network Structures; 3.4.1 Joint BBN Structure
3.4.2 Disjoint (Pairwise) Bayesian Belief Network Structure3.5 Bayesian Updating; 3.5.1 Fully Specified Joint BBN; 3.5.2 Partially Specified Disjoint BBN; 3.6 Certain Event; 3.7 Categorical Variable; 3.8 Chain (Product) Rule; 3.9 Collectively Exhaustive; 3.10 Combinations and Permutations; 3.10.1 Combinations; 3.10.2 Permutations; 3.11 Complement and Complement Rule; 3.12 Conditional and Unconditional Probability; 3.12.1 Conditional Probability; 3.12.2 Unconditional Probability; 3.13 Counting and Countable Set and Uncountable Set; 3.13.1 Counting; 3.13.2 Countable and Countable Set