Bayes theory / J.A. Hartigan.
Series Springer series in statisticsEditor: New York : Springer-Verlag, c1983Descripción: xii, 145 p. : ill. ; 24 cmTema(s): Mathematical statisticsOtra clasificación: *CODIGO*CHAPTER [1] -- Theories of Probability [1] -- 1.0. Introduction [1] -- 1.1. Logical Theories: Laplace [1] -- 12. 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] -- 1.7. Subjective Theories: Good -- 1.8. All the Probabilities [8] -- 1.9. Infinite Axioms [10] -- 1.10. Probability and Similarity [11] -- 1.11. References [13] -- CHAPTER [2] -- Axioms [14] -- 2.0. Notation [14] -- 2.1. Probability Axioms [14] -- 22. Prespaces and Rings [16] -- 2.3. Random Variables [18] -- 2.4. Probable Bets [18] -- 2.5. Comparative Probability [20] -- 2.6. Problems [20] -- 2.7. References [22] -- CHAPTER [3] -- Conditional Probability [23] -- 3.0. Introduction [23] -- 3.1. Axioms of Conditional Probability [24] -- 3.2. Product Probabilities [26] -- 3.3. Quotient Probabilities [27] -- 3.4. Marginalization Paradoxes [28] -- 3.5. Bayes Theorem [29] -- 3.6. Binomial Conditional Probability [31] -- 3.7. Problems [32] -- 3.8. References [33] -- CHAPTER [4] -- Convergence [34] -- 4.0. Introduction [34] -- 4.1. Convergence Definitions [34] -- 4.2. Mean Convergence of Conditional Probabilities [35] -- 4.3. Almost Sure Convergence of Conditional Probabilities [36] -- 4.4. Consistency of Posterior Distributions [38] -- 4.5. Binomial Case [38] -- 4.6. Exchangeable Sequences [40] -- 4.7. Problems [42] -- 4.8. References [43] -- CHAPTER [5] -- Making Probabilities [44] -- 5.0.Introduction [44] -- 5.1.Information [44] -- 5.2.Maximal Learning Probabilities [45] -- 5.3.Invariance [47] -- 5.4.The Jeffreys Density [48] -- 5.5.Similarity Probability [50] -- 5.6.Problems [53] -- 5.7.References [55] -- CHAPTER [6] -- Decision Theory [56] -- 6.0.Introduction [56] -- 6.1.Admissible Decisions [56] -- 6.2.Conditional Bayes Decisions [58] -- 6.3.Admissibility of Bayes Decisions [59] -- 6.4.Variations on the Definition of Admissibility [61] -- 6.5.Problems [62] -- 6.6.References [62] -- CHAPTER [7] -- Uniformity Criteria for Selecting Decisions [63] -- 7.0. Introduction [63] -- 7.1. Bayes Estimates Are Biased or Exact [63] -- 7.2. Unbiased Location Estimates [64] -- 7.3. Unbiased Bayes Tests [65] -- 7.4. Confidence Regions [67] -- 7.5. One-Sided Confidence Intervals Are Not Unitary Bayes [68] -- 7.6. Conditional Bets [68] -- 7.7. Problems [69] -- 7.8. References [71] -- CHAPTER [8] -- Exponential Families [72] -- 8.0. Introduction [72] -- 8.1. Examples of Exponential Families [73] -- 8.2. Prior Distributions for the Exponential Family [73] -- 8.3. Normal Location [74] -- 8.4. Binomial [76] -- 8.5. Poisson [79] -- 8.6. Normal Location and Scale [79] -- 8.7. Problems [82] -- 8.8. References [83] -- CHAPTER [9] -- Many Normal Means [84] -- 9.0. Introduction [84] -- 9.1. Baranchik’s Theorem [84] -- 9.2. Bayes Estimates Beating the Straight Estimate [86] -- 9.3. Shrinking towards the Mean [88] -- 9.4. A Random Sample of Means [89] -- 9.5. When Most of the Means Are Small [89] -- 9.6. Multivariate Means [91] -- 9.7. Regression [92] -- 9.8. Many Means, Unknown Variance [92] -- 9.9. Variance Components, One Way Analysis of Variance [93] -- 9.10. Problems [94] -- 9.11. References [95] -- CHAPTER [10] -- The Multinomial Distribution [96] -- 10.0. Introduction [96] -- 10.1. Dirichlet Priors [96] -- 10.2. Admissibility of Maximum Likelihood, Multinomial Case [97] -- 10.3. Inadmissibility of Maximum Likelihood, Poisson Case [99] -- 10.4. Selection of Dirichlet Priors [100] -- 10.5. Two Stage Poisson Models [101] -- 10.6. Multinomials with Clusters [101] -- -- -- 10.7. Multinomials with Similarities [102] -- 10.8. Contingency Tables [103] -- 10.9. Problems [104] -- 10.10. References [105] -- CHAPTER [11] -- Asymptotic Normality of Posterior Distributions107 -- 11.0. Introduction [107] -- 11.1. A Crude Demonstration of Asymptotic Normality [108] -- 11.2. Regularity Conditions for Asymptotic Normality [108] -- 11.3. Pointwise Asymptotic Normality [111] -- 11.4. Asymptotic Normality of Martingale Sequences [113] -- 11.5. Higher Order Approximations to Posterior Densities [115] -- 11.6. Problems [116] -- 11.7. References [118] -- CHAPTER [12] -- Robustness of Bayes Methods [119] -- 12.0. Introduction [119] -- 12.1. Intervals of Probabilities [120] -- 12.2. Intervals of Means [120] -- 12.3. Intervals of Risk [121] -- 12.4. Posterior Variances [122] -- 12.5. Intervals of Posterior Probabilities [122] -- 12.6. Asymptotic Behavior of Posterior Intervals [123] -- 12.7. Asymptotic Intervals under Asymptotic Normality [124] -- 12.8. A More General Range of Probabilities [125] -- 12.9. Problems [126] -- 12.10. References [126] -- CHAPTER [13] -- Nonparametric Bayes Procedures [127] -- 13.0. Introduction [127] -- 13.1. The Dirichlet Process [127] -- 13.2 The Dirichlet Process on (0,1) [130] -- 13.3. Bayes Theorem for a Dirichlet Process [131] -- 13.4. The Empirical Process [132] -- 13.5. Subsample Methods [133] -- 13.6. The Tolerance Process [134] -- 13.7. Problems [134] -- 13.8. References [135] -- Author Index [137] -- Subject Index [141] --
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode |
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Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 62 H329 (Browse shelf) | Available | A-9363 |
Includes bibliographies and indexes.
CHAPTER [1] --
Theories of Probability [1] --
1.0. Introduction [1] --
1.1. Logical Theories: Laplace [1] --
12. 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] --
1.7. Subjective Theories: Good --
1.8. All the Probabilities [8] --
1.9. Infinite Axioms [10] --
1.10. Probability and Similarity [11] --
1.11. References [13] --
CHAPTER [2] --
Axioms [14] --
2.0. Notation [14] --
2.1. Probability Axioms [14] --
22. Prespaces and Rings [16] --
2.3. Random Variables [18] --
2.4. Probable Bets [18] --
2.5. Comparative Probability [20] --
2.6. Problems [20] --
2.7. References [22] --
CHAPTER [3] --
Conditional Probability [23] --
3.0. Introduction [23] --
3.1. Axioms of Conditional Probability [24] --
3.2. Product Probabilities [26] --
3.3. Quotient Probabilities [27] --
3.4. Marginalization Paradoxes [28] --
3.5. Bayes Theorem [29] --
3.6. Binomial Conditional Probability [31] --
3.7. Problems [32] --
3.8. References [33] --
CHAPTER [4] --
Convergence [34] --
4.0. Introduction [34] --
4.1. Convergence Definitions [34] --
4.2. Mean Convergence of Conditional Probabilities [35] --
4.3. Almost Sure Convergence of Conditional Probabilities [36] --
4.4. Consistency of Posterior Distributions [38] --
4.5. Binomial Case [38] --
4.6. Exchangeable Sequences [40] --
4.7. Problems [42] --
4.8. References [43] --
CHAPTER [5] --
Making Probabilities [44] --
5.0.Introduction [44] --
5.1.Information [44] --
5.2.Maximal Learning Probabilities [45] --
5.3.Invariance [47] --
5.4.The Jeffreys Density [48] --
5.5.Similarity Probability [50] --
5.6.Problems [53] --
5.7.References [55] --
CHAPTER [6] --
Decision Theory [56] --
6.0.Introduction [56] --
6.1.Admissible Decisions [56] --
6.2.Conditional Bayes Decisions [58] --
6.3.Admissibility of Bayes Decisions [59] --
6.4.Variations on the Definition of Admissibility [61] --
6.5.Problems [62] --
6.6.References [62] --
CHAPTER [7] --
Uniformity Criteria for Selecting Decisions [63] --
7.0. Introduction [63] --
7.1. Bayes Estimates Are Biased or Exact [63] --
7.2. Unbiased Location Estimates [64] --
7.3. Unbiased Bayes Tests [65] --
7.4. Confidence Regions [67] --
7.5. One-Sided Confidence Intervals Are Not Unitary Bayes [68] --
7.6. Conditional Bets [68] --
7.7. Problems [69] --
7.8. References [71] --
CHAPTER [8] --
Exponential Families [72] --
8.0. Introduction [72] --
8.1. Examples of Exponential Families [73] --
8.2. Prior Distributions for the Exponential Family [73] --
8.3. Normal Location [74] --
8.4. Binomial [76] --
8.5. Poisson [79] --
8.6. Normal Location and Scale [79] --
8.7. Problems [82] --
8.8. References [83] --
CHAPTER [9] --
Many Normal Means [84] --
9.0. Introduction [84] --
9.1. Baranchik’s Theorem [84] --
9.2. Bayes Estimates Beating the Straight Estimate [86] --
9.3. Shrinking towards the Mean [88] --
9.4. A Random Sample of Means [89] --
9.5. When Most of the Means Are Small [89] --
9.6. Multivariate Means [91] --
9.7. Regression [92] --
9.8. Many Means, Unknown Variance [92] --
9.9. Variance Components, One Way Analysis of Variance [93] --
9.10. Problems [94] --
9.11. References [95] --
CHAPTER [10] --
The Multinomial Distribution [96] --
10.0. Introduction [96] --
10.1. Dirichlet Priors [96] --
10.2. Admissibility of Maximum Likelihood, Multinomial Case [97] --
10.3. Inadmissibility of Maximum Likelihood, Poisson Case [99] --
10.4. Selection of Dirichlet Priors [100] --
10.5. Two Stage Poisson Models [101] --
10.6. Multinomials with Clusters [101] --
--
--
10.7. Multinomials with Similarities [102] --
10.8. Contingency Tables [103] --
10.9. Problems [104] --
10.10. References [105] --
CHAPTER [11] --
Asymptotic Normality of Posterior Distributions107 --
11.0. Introduction [107] --
11.1. A Crude Demonstration of Asymptotic Normality [108] --
11.2. Regularity Conditions for Asymptotic Normality [108] --
11.3. Pointwise Asymptotic Normality [111] --
11.4. Asymptotic Normality of Martingale Sequences [113] --
11.5. Higher Order Approximations to Posterior Densities [115] --
11.6. Problems [116] --
11.7. References [118] --
CHAPTER [12] --
Robustness of Bayes Methods [119] --
12.0. Introduction [119] --
12.1. Intervals of Probabilities [120] --
12.2. Intervals of Means [120] --
12.3. Intervals of Risk [121] --
12.4. Posterior Variances [122] --
12.5. Intervals of Posterior Probabilities [122] --
12.6. Asymptotic Behavior of Posterior Intervals [123] --
12.7. Asymptotic Intervals under Asymptotic Normality [124] --
12.8. A More General Range of Probabilities [125] --
12.9. Problems [126] --
12.10. References [126] --
CHAPTER [13] --
Nonparametric Bayes Procedures [127] --
13.0. Introduction [127] --
13.1. The Dirichlet Process [127] --
13.2 The Dirichlet Process on (0,1) [130] --
13.3. Bayes Theorem for a Dirichlet Process [131] --
13.4. The Empirical Process [132] --
13.5. Subsample Methods [133] --
13.6. The Tolerance Process [134] --
13.7. Problems [134] --
13.8. References [135] --
Author Index [137] --
Subject Index [141] --
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