Bayes Theory

1. Front Matter

   Pages i-xii

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2. Theories of Probability

   • J. A. Hartigan

   Pages 1-13

3. Axioms

   • J. A. Hartigan

   Pages 14-22

4. Conditional Probability

   • J. A. Hartigan

   Pages 23-33

5. Convergence

   • J. A. Hartigan

   Pages 34-43

6. Making Probabilities

   • J. A. Hartigan

   Pages 44-55

7. Decision Theory

   • J. A. Hartigan

   Pages 56-62

8. Uniformity Criteria for Selecting Decisions

   • J. A. Hartigan

   Pages 63-71

9. Exponential Families

   • J. A. Hartigan

   Pages 72-83

10. Many Normal Means

    • J. A. Hartigan

    Pages 84-95

11. The Multinomial Distribution

    • J. A. Hartigan

    Pages 96-106

12. Asymptotic Normality of Posterior Distributions

    • J. A. Hartigan

    Pages 107-118

13. Robustness of Bayes Methods

    • J. A. Hartigan

    Pages 119-126

14. Nonparametric Bayes Procedures

    • J. A. Hartigan

    Pages 127-135

15. Back Matter

    Pages 137-145

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This book is based on lectures given at Yale in 1971-1981 to students prepared with a course in measure-theoretic probability. It contains one technical innovation-probability distributions in which the total probability is infinite. Such improper distributions arise embarras­ singly frequently in Bayes theory, especially in establishing correspondences between Bayesian and Fisherian techniques. Infinite probabilities create interesting complications in defining conditional probability and limit concepts. The main results are theoretical, probabilistic conclusions derived from probabilistic assumptions. A useful theory requires rules for constructing and interpreting probabilities. Probabilities are computed from similarities, using a formalization of the idea that the future will probably be like the past. Probabilities are objectively derived from similarities, but similarities are sUbjective judgments of individuals. Of course the theorems remain true in any interpretation of probability that satisfies the formal axioms. My colleague David Potlard helped a lot, especially with Chapter 13. Dan Barry read proof. vii Contents CHAPTER 1 Theories of Probability 1. 0. Introduction 1 1. 1. Logical Theories: Laplace 1 1. 2. Logical Theories: Keynes and Jeffreys 2 1. 3. Empirical Theories: Von Mises 3 1. 4. Empirical Theories: Kolmogorov 5 1. 5. Empirical Theories: Falsifiable Models 5 1. 6. Subjective Theories: De Finetti 6 7 1. 7. Subjective Theories: Good 8 1. 8. All the Probabilities 10 1. 9. Infinite Axioms 11 1. 10. Probability and Similarity 1. 11. References 13 CHAPTER 2 Axioms 14 2. 0. Notation 14 2. 1. Probability Axioms 14 2. 2.

• Bayessches Verfahren
• Finite
• Logic
• boundary element method
• conditional probability
• form
• innovation
• object
• probability
• probability axioms
• probability distribution
• proof
• similarity
• techniques
• theorem

"Hartigan provides a carefully referenced discussion that contains both supporting concepts as well as a presentation of Bayes theory."
(Choice)

• Department of Statistics, Yale University, New Haven, USA

  J. A. Hartigan

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