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1 SpringerBriefs in Statistics For further volumes:
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3 Jeff Grover Strategic Economic Decision-Making Using Bayesian Belief Networks to Solve Complex Problems
4 Jeff Grover Maple Crest Way 512 Elizabethtown, Kentucky, USA ISSN X ISSN (electronic) ISBN ISBN (ebook) DOI / Springer New York Heidelberg Dordrecht London Library of Congress Control Number: # Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (
5 Sergeant First Class Charles V. Lang, IV (U.S. Army, Retired) Friend
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7 Contents 1 An Introduction to Bayes Theorem and Bayesian Belief Networks (BBN) Introduction to Bayes Theorem and BBN The Identification of the Truth The Motivation for This Book The Intent of This Book The Utility of Bayes Theorem Inductive Verses Deductive Logic Popper s Logic of Scientific Discovery Frequentist Verses Bayesian (Subjective) Views Frequentist to Subjectivist Philosophy Bayesian Philosophy... 8 References A Literature Review of Bayes Theorem and Bayesian Belief Networks (BBN) Introduction to the Bayes Theorem Evolution Early 1900s s 1930s s 1950s s Mid 1980s BBN Evolution Financial Economics, Accounting, and Operational Risks Safety, Accident Analysis, and Prevention Engineering and Safety Risk Analysis Ecology Human Behavior Behavioral Sciences and Marketing vii
8 viii Contents Decision Support Systems (DSS) with Expert Systems (ES) and Applications, Information Sciences, Intelligent Data Analysis, Neuroimaging, Environmental Modeling and Software, and Industrial Ergonomics Cognitive Science Medical, Health, Dental, and Nursing Environmental Studies Miscellaneous: Politics, Geriatrics, Space Policy, and Language and Speech Current Government and Commercial Users of BBN References Statistical Properties of Bayes Theorem Introduction to Statistical Terminology Bayes Theorem Proof A Bayes Theorem Proof with Two Events, AandB A Step-by-Step Explanation of the Two Event Bayes Theorem Proof A Bayes Theorem Proof with Three Events, A,B,&C Independence and Conditional Independence Evaluation Statistical Definitions Axioms of Probability Bayes Theorem Combinations and Permutations Conditional and Unconditional Probability Counting, Countable and Uncountable Set Complement and Complement Rule Disjoint or Mutually Exclusive Events/Sets Event Factorial Intersection and Union (of Sets) Joint and Marginal Probability Distribution Mean, Arithmetic Mean Outcome Space Parameter Partition Population Prior and Posterior Probabilities Probability and Probability Sample Product (Chain) Rule
9 Contents ix Sample, Sample Space, Random Sample, Simple Random Sample, Random Experiment (Event), and Random Variable Real Number Set, Subset, Member of a Set, and Empty Set Theories of Probability Unit Venn Diagram TheAlgebra of Sets Theorem 1: For Any Subsets, A, B, & C of a Set U the Following Equations Are Identities Theorem 2: For Any Subsets, A and B of a Set U the Following Equations Are Identities References Bayesian Belief Networks (BBN) Experimental Protocol Introduction BBN Experimental Protocol Characteristics of a Random Experiment Bayes Research Methodology Conducting a Bayesian Experiment References Manufacturing Example Scenario Experimental Protocol Conclusions Posterior Probabilities Inverse Probabilities References Political Science Example Scenario Experimental Protocol Conclusions Posterior Probabilities Inverse Probabilities Gambling Example Scenario Experimental Protocol Conclusions Posterior Probabilities Inverse Probabilities... 65
10 x Contents 8 Publicly Traded Company Default Example Scenario Experimental Protocol Conclusions Posterior Probabilities Inverse Probabilities Insurance Risk Levels Example Scenario Experimental Protocol Conclusions Posterior Probabilities Inverse Probabilities Acts of Terrorism Example Scenario Experimental Protocol Conclusions Posterior Probabilities Inverse Probabilities Currency Wars Example Scenario Experimental Protocol Conclusions Posterior Probabilities Inverse Probabilities References College Entrance Exams Example Scenario Experimental Protocol Conclusions Posterior Probabilities Inverse Probabilities Special Forces Assessment and Selection (SFAS) One-Stage Example Scenario Experimental Protocol Conclusions Posterior Probabilities Inverse Probabilities Reference
11 Contents xi 14 Special Forces Assessment and Selection (SFAS) Two-Stage Example Scenario Experimental Protocol Conclusions Posterior Probabilities Inverse Probabilities References Index
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