(SpringerBriefs in Statistics 9)
Jeff Grover  (auth.)-
Strategic Economic Decision-Making
_ Using Bayesian Belief Networks to Solve Complex Problems
-Springer New York (2013)



SSN 2191-544X ISSN 2191-5458 (electronic)
ISBN 978-1-4614-6039-8 ISBN 978-1-4614-6040-4 (eBook)
DOI 10.1007/978-1-4614-6040-4
Springer New York Heidelberg Dordrecht London
Library of Congress Control Number: 2012951657
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1 An Introduction to Bayes’ Theorem and Bayesian
Belief Networks (BBN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction to Bayes’ Theorem and BBN . . . . . . . . . . . . . . . . . 1
1.2 The Identification of the Truth. . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 The Motivation for This Book. . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 The Intent of This Book. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 The Utility of Bayes’ Theorem. . . . . . . . . . . . . . . . . . . . . . . . . 5
1.6 Inductive Verses Deductive Logic . . . . . . . . . . . . . . . . . . . . . . . 5
1.7 Popper’s Logic of Scientific Discovery . . . . . . . . . . . . . . . . . . . 6
1.8 Frequentist Verses Bayesian (Subjective) Views . . . . . . . . . . . . . 6
1.8.1 Frequentist to Subjectivist Philosophy . . . . . . . . . . . . . . . 6
1.8.2 Bayesian Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 A Literature Review of Bayes’ Theorem
and Bayesian Belief Networks (BBN) . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Introduction to the Bayes’ Theorem Evolution . . . . . . . . . . . . . . 11
2.1.1 Early 1900s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.2 1920s–1930s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.3 1940s–1950s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.4 1960s–Mid 1980s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 BBN Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1 Financial Economics, Accounting,
and Operational Risks . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.2 Safety, Accident Analysis, and Prevention . . . . . . . . . . 15
2.2.3 Engineering and Safety . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.4 Risk Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.5 Ecology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.6 Human Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.7 Behavioral Sciences and Marketing. . . . . . . . . . . . . . . 16
vii
2.2.8 Decision Support Systems (DSS) with Expert
Systems (ES) and Applications, Information
Sciences, Intelligent Data Analysis, Neuroimaging,
Environmental Modeling and Software, and
Industrial Ergonomics . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.9 Cognitive Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.10 Medical, Health, Dental, and Nursing . . . . . . . . . . . . . . 18
2.2.11 Environmental Studies . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.12 Miscellaneous: Politics, Geriatrics,
Space Policy, and Language and Speech . . . . . . . . . . . . 18
2.3 Current Government and Commercial Users of BBN . . . . . . . . . 19
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Statistical Properties of Bayes’ Theorem . . . . . . . . . . . . . . . . . . . . 29
3.1 Introduction to Statistical Terminology . . . . . . . . . . . . . . . . . . . 29
3.2 Bayes’ Theorem Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.1 A Bayes’ Theorem Proof with Two Events,
A and B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.2 A Step-by-Step Explanation of the Two
Event Bayes’ Theorem Proof . . . . . . . . . . . . . . . . . . . . . 30
3.2.3 A Bayes’ Theorem Proof with Three Events,
A, B, & C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.4 Independence and Conditional Independence
Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 Statistical Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3.1 Axioms of Probability . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3.2 Bayes’ Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3.3 Combinations and Permutations . . . . . . . . . . . . . . . . . . 33
3.3.4 Conditional and Unconditional Probability . . . . . . . . . . 33
3.3.5 Counting, Countable and Uncountable Set . . . . . . . . . . . 34
3

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4 Bayesian Belief Networks (BBN) Experimental Protocol . . . . . . . . 43
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 BBN Experimental Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3 Characteristics of a Random Experiment . . . . . . . . . . . . . . . . . . 43
4.4 Bayes’ Research Methodology . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.5 Conducting a Bayesian Experiment . . . . . . . . . . . . . . . . . . . . . . 45
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5 Manufacturing Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.1 Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2 Experimental Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.3.1 Posterior Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.3.2 Inverse Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6 Political Science Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.1 Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.2 Experimental Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.3.1 Posterior Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.3.2 Inverse Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7 Gambling Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
7.1 Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
7.2 Experimental Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
7.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.3.1 Posterior Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.3.2 Inverse Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Contents ix
8 Publicly Traded Company Default Example . . . . . . . . . . . . . . . . . . 67
8.1 Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
8.2 Experimental Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
8.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
8.3.1 Posterior Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 71
8.3.2 Inverse Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
9 Insurance Risk Levels Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
9.1 Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
9.2 Experimental Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
9.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
9.3.1 Posterior Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 77
9.3.2 Inverse Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
10.1 Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
10.2 Experimental Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
10.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
10.3.1 Posterior Probabilities . . . . . . . . . . . . . . . . . . . . . . . . 83
10.3.2 Inverse Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 84
11 Currency Wars Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
11.1 Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
11.2 Experimental Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
11.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
11.3.1 Posterior Probabilities . . . . . . . . . . . . . . . . . . . . . . . . 89
11.3.2 Inverse Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 90
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
12 College Entrance Exams Example . . . . . . . . . . . . . . . . . . . . . . . . . 91
12.1 Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
12.2 Experimental Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
12.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
12.3.1 Posterior Probabilities . . . . . . . . . . . . . . . . . . . . . . . . 95
12.3.2 Inverse Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 95
13 Special Forces Assessment and Selection (SFAS)
One-Stage Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
13.1 Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
13.2 Experimental Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
13.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
13.3.1 Posterior Probabilities . . . . . . . . . . . . . . . . . . . . . . . . 101
13.3.2 Inverse Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
x Contents
10 Acts of Terrorism Example . . . . . . . . . . . . . . . . . . . . . . . . . . 79 (AOT)
14 Special Forces Assessment and Selection (SFAS)
Two-Stage Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
14.1 Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
14.2 Experimental Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
14.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
14.3.1 Posterior Probabilities . . . . . . . . . . . . . . . . . . . . . . . . 110
14.3.2 Inverse Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 111
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115