Author | Hartigan, J. A. author |
---|---|
Title | Bayes Theory [electronic resource] / by J. A. Hartigan |
Imprint | New York, NY : Springer New York, 1983 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-8242-3 |
Descript | XII, 146 p. online resource |
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. Baranchikโs 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