Bayes Theory

Paperback (Softcover reprint of the original 1st ed. 1983)
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Editorial Reviews

From the Publisher
"Hartigan provides a carefully referenced discussion that contains both supporting concepts as well as a presentation of Bayes theory."
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Product Details

  • ISBN-13: 9781461382447
  • Publisher: Springer New York
  • Publication date: 7/31/2012
  • Series: Springer Series in Statistics
  • Edition description: Softcover reprint of the original 1st ed. 1983
  • Edition number: 1
  • Pages: 160
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.34 (d)

Table of Contents

1 Theories of Probability.- 1.0. Introduction.- 1.1. Logical Theories: Laplace.- 1.2. Logical Theories: Keynes and Jeffreys.- 1.3. Empirical Theories: Von Mises.- 1.4. Empirical Theories: Kolmogorov.- 1.5. Empirical Theories: Falsifiable Models.- 1.6. Subjective Theories: De Finetti.- 1.7. Subjective Theories: Good.- 1.8. All the Probabilities.- 1.9. Infinite Axioms.- 1.10. Probability and Similarity.- 1.11. References.- 2 Axioms.- 2.0. Notation.- 2.1. Probability Axioms.- 2.2. Prespaces and Rings.- 2.3. Random Variables.- 2.4. Probable Bets.- 2.5. Comparative Probability.- 2.6. Problems.- 2.7. References.- 3 Conditional Probability.- 3.0. Introduction.- 3.1. Axioms of Conditional Probability.- 3.2. Product Probabilities.- 3.3. Quotient Probabilities.- 3.4. Marginalization Paradoxes.- 3.5. Bayes Theorem.- 3.6. Binomial Conditional Probability.- 3.7. Problems.- 3.8. References.- 4 Convergence.- 4.0. Introduction.- 4.1. Convergence Definitions.- 4.2. Mean Convergence of Conditional Probabilities.- 4.3. Almost Sure Convergence of Conditional Probabilities.- 4.4. Consistency of Posterior Distributions.- 4.5. Binomial Case.- 4.6. Exchangeable Sequences.- 4.7. Problems.- 4.8. References.- 5 Making Probabilities.- 5.0. Introduction.- 5.1. Information.- 5.2. Maximal Learning Probabilities.- 5.3. Invariance.- 5.4. The Jeffreys Density.- 5.5. Similarity Probability.- 5.6. Problems.- 5.7. References.- 6 Decision Theory.- 6.0. Introduction.- 6.1. Admissible Decisions.- 6.2. Conditional Bayes Decisions.- 6.3. Admissibility of Bayes Decisions.- 6.4. Variations on the Definition of Admissibility.- 6.5. Problems.- 6.6. References.- 7 Uniformity Criteria for Selecting Decisions.- 7.0. Introduction.- 7.1. Bayes Estimates Are Biased or Exact.- 7.2. Unbiased Location Estimates.- 7.3. Unbiased Bayes Tests.- 7.4. Confidence Regions.- 7.5. One-Sided Confidence Intervals Are Not Unitary Bayes.- 7.6. Conditional Bets.- 7.7. Problems.- 7.8. References.- 8 Exponential Families.- 8.0. Introduction.- 8.1. Examples of Exponential Families.- 8.2. Prior Distributions for the Exponential Family.- 8.3. Normal Location.- 8.4. Binomial.- 8.5. Poisson.- 8.6. Normal Location and Scale.- 8.7. Problems.- 8.8. References.- 9 Many Normal Means.- 9.0. Introduction.- 9.1. Baranchik’s Theorem.- 9.2. Bayes Estimates Beating the Straight Estimate.- 9.3. Shrinking towards the Mean.- 9.4. A Random Sample of Means.- 9.5. When Most of the Means Are Small.- 9.6. Multivariate Means.- 9.7. Regression.- 9.8. Many Means, Unknown Variance.- 9.9. Variance Components, One Way Analysis of Variance.- 9.10. Problems.- 9.11. References.- 10 The Multinomial Distribution.- 10.0. Introduction.- 10.1. Dirichlet Priors.- 10.2. Admissibility of Maximum Likelihood, Multinomial Case.- 10.3. Inadmissibility of Maximum Likelihood, Poisson Case.- 10.4. Selection of Dirichlet Priors.- 10.5. Two Stage Poisson Models.- 10.6. Multinomials with Clusters.- 10.7. Multinomials with Similarities.- 10.8. Contingency Tables.- 10.9. Problems.- 10.10. References.- 11 Asymptotic Normality of Posterior Distributions.- 11.0. Introduction.- 11.1. A Crude Demonstration of Asymptotic Normality.- 11.2. Regularity Conditions for Asymptotic Normality.- 11.3. Pointwise Asymptotic Normality.- 11.4. Asymptotic Normality of Martingale Sequences.- 11.5. Higher Order Approximations to Posterior Densities.- 11.6. Problems.- 11.7. References.- 12 Robustness of Bayes Methods.- 12.0. Introduction.- 12.1. Intervals of Probabilities.- 12.2. Intervals of Means.- 12.3. Intervals of Risk.- 12.4. Posterior Variances.- 12.5. Intervals of Posterior Probabilities.- 12.6. Asymptotic Behavior of Posterior Intervals.- 12.7. Asymptotic Intervals under Asymptotic Normality.- 12.8. A More General Range of Probabilities.- 12.9. Problems.- 12.10. References.- 13 Nonparametric Bayes Procedures.- 13.0. Introduction.- 13.1. The Dirichlet Process.- 13.2 The Dirichlet Process on (0, 1).- 13.3. Bayes Theorem for a Dirichlet Process.- 13.4. The Empirical Process.- 13.5. Subsample Methods.- 13.6. The Tolerance Process.- 13.7. Problems.- 13.8. References.- Author Index.
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