Elements of Bayesian statistics

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Elements of Bayesian statistics / Jean Pierre Florens, Michel Mouchart, Jean-Marie Rolin

資料種別:

図書

出版情報:

New York : M. Dekker, c1990

形態:

xxxi, 499 p. ; 24 cm

シリーズ名:

Monographs and textbooks in pure and applied mathematics ; 134 <BA00046446>

著者名:

ISBN:

9780824781231 [0824781236]

書誌ID:

BA10001455

子書誌情報

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書誌詳細

注記:

Bibliography: p. 463-487
Includes indexes

主題:

Bayesian statistical decision theory

言語:

英語

目次情報:

Preface

Notation

Basic Tools and Notation from Probability Theory / 0.：

Introduction / 0.1.：

Measurable Spaces / 0.2.：

[sigma]-Fields / 0.2.1.：

Measurable Functions / 0.2.2.：

Product of Measurable Spaces / 0.2.3.：

Monotone Class Theorems / 0.2.4.：

Probability Spaces / 0.3.：

Measures and Integrals / 0.3.1.：

Probabilities. Expectations. Null Sets / 0.3.2.：

Transition and Product Probability / 0.3.3.：

Conditional Expectation / 0.3.4.：

Densities / 0.3.5.：

Bayesian Experiments / 1.：

The Basic Concepts of Bayesian Experiments / 1.1.：

General Definitions / 1.2.1.：

Dominated Experiments / 1.2.2.：

Three Remarks on Regular and Dominated Experiments / 1.2.3.：

A Remark Regarding the Interpretation of Bayesian Experiments / 1.2.4.：

A Remark on Sampling Theory and Bayesian Methods / 1.2.5.：

A Remark Regarding So-called "Improper" Prior Distributions / 1.2.6.：

Families of Bayesian Experiments / 1.2.7.：

Some Examples of Bayesian Experiments / 1.3.：

Reduction of Bayesian Experiments / 1.4.：

Marginal Experiments / 1.4.1.：

Conditional Experiment / 1.4.3.：

Complementary Reductions / 1.4.4.：

Dominance in Reduced Experiments / 1.4.5.：

Admissible Reductions: Sufficiency and Ancillarity / 2.：

Conditional Independence / 2.1.：

Definition of Conditional Independence / 2.2.1.：

Null Sets and Completion / 2.2.3.：

Basic Properties of Conditional Independence / 2.2.4.：

Conditional Independence and Densities / 2.2.5.：

Conditional Independence as Point Properties / 2.2.6.：

Admissible Reductions of an Unreduced Experiment / 2.3.：

Admissible Reductions on the Sample Space / 2.3.1.：

Admissible Reductions on the Parameter Space / 2.3.3.：

Some Comments on the Definitions / 2.3.4.：

Elementary Properties of Sufficiency and Ancillarity / 2.3.5.：

Sufficiency and Ancillarity in a Dominated Experiment / 2.3.6.：

Sampling Theory and Bayesian Methods / 2.3.7.：

A First Result on the Relations between Sufficiency and Ancillarity / 2.3.8.：

Admissible Reductions in Reduced Experiments / 3.：

Admissible Reduction in Marginal Experiments / 3.1.：

Basic Concepts / 3.2.1.：

Sufficiency and Ancillarity in Unreduced and in Marginal Experiments / 3.2.3.：

A Remark on "Partial" Sufficiency / 3.2.4.：

Admissible Reductions in Conditional Experiments / 3.3.：

Reductions in the Sample Space / 3.3.1.：

Reductions in the Parameter Space / 3.3.3.：

Elementary Properties / 3.3.4.：

Relationships between Sufficiency and Ancillarity / 3.3.5.：

Sufficiency and Ancillarity in a Dominated Reduced Experiment / 3.3.6.：

Jointly Admissible Reductions / 3.4.：

Mutual Sufficiency / 3.4.1.：

Mutual Exogeneity / 3.4.2.：

Bayesian Cut / 3.4.3.：

Joint Reductions in a Dominated Experiment / 3.4.4.：

Joint Reductions in a Conditional Experiment / 3.4.5.：

Some Examples / 3.4.6.：

Comparison of Experiments / 3.5.：

Comparison on the Sample Space: Sufficiency / 3.5.1.：

Comparison on the Parameter Space: Encompassing / 3.5.2.：

Optimal Reductions: Maximal Ancillarity and Minimal Sufficiency / 4.：

Maximal Ancillarity / 4.1.：

Projections of [sigma]-Fields / 4.3.：

Definition and Elementary Properties / 4.3.1.：

Projections and Conditional Independence / 4.3.3.：

Minimal Sufficiency / 4.4.：

Minimal Sufficiency in Unreduced and in Marginal Experiments / 4.4.1.：

Elementary Properties of Minimal Sufficiency / 4.4.2.：

Minimal Sufficiency in a Dominated Experiment / 4.4.3.：

Minimal Sufficiency in Conditional Experiment / 4.4.4.：

Optimal Mutual Sufficiency / 4.4.6.：

Identification Among [sigma]-Fields / 4.5.：

Identification in Bayesian Experiments / 4.6.：

Identification in a Reduced Experiment / 4.6.1.：

Exact and Totally Informative Experiments / 4.6.2.：

Punctual Exact Estimability / 4.8.：

Optimal Reductions: Further Results / 5.：

Measurable Separability / 5.1.：

Measurable Separability in Bayesian Experiments / 5.3.：

Measurably Separated Bayesian Experiment / 5.3.1.：

Basu Second Theorem / 5.3.2.：

Strong Identification of [sigma]-Fields / 5.3.3.：

Definition and General Properties / 5.4.1.：

Strong Identification and Conditional Independence / 5.4.2.：

Minimal Splitting / 5.4.3.：

Completeness in Bayesian Experiments / 5.5.：

Completeness and Sufficiency / 5.5.1.：

Completeness and Ancillarity / 5.5.2.：

Successive Reductions of a Bayesian Experiment / 5.5.3.：

Identifiability of Mixtures / 5.5.4.：

Sequential Experiments / 6.：

Sequences of Conditional Independences / 6.1.：

Definition of Sequential Experiments / 6.3.：

Admissible Reductions in Sequential Experiments / 6.3.2.：

Transitivity / 6.4.：

Basic Theory / 6.4.1.：

Markovian Property and Transitivity / 6.4.2.：

Relations Among Admissible Reductions / 6.5.：

Admissible Reductions in Joint Reductions / 6.5.1.：

The Role of Transitivity: Further Results / 6.6.：

Weakening of Transitivity Conditions / 6.6.1.：

Necessity of Transitivity Conditions / 6.6.2.：

Asymptotic Experiments / 7.：

Limit of Sequences of Conditional Independences / 7.1.：

Asymptotically Admissible Reductions / 7.3.：

Asymptotic Properties of Sequential Experiments / 7.3.1.：

Asymptotic Sufficiency / 7.3.2.：

Asymptotic Admissibility of Joint Reductions / 7.3.3.：

Asymptotically Admissible Reductions in Conditional Experiments / 7.3.4.：

Asymptotic Exact Estimability / 7.4.：

Exact Estimability and Bayesian Consistency / 7.4.1.：

Estimability of Discrete [sigma]-Fields / 7.4.2.：

Mutual Conditional Independence and Conditional 0-1 Laws / 7.6.：

Mutual Conditional Independence / 7.6.1.：

Sifted Sequences of [sigma]-Fields / 7.6.2.：

Tail-Sufficient and Independent Bayesian Experiments / 7.7.：

Bayesian Tail-Sufficiency / 7.7.1.：

Bayesian Independence / 7.7.2.：

Independent Tail-Sufficient Bayesian Experiments / 7.7.3.：

An Example / 7.8.：

Global and Sequential Analysis / 7.8.1.：

Asymptotic Analysis / 7.8.2.：

The Case [beta] = [infinity] / 7.8.3.：

The Case [beta less than sign infinity] / 7.8.4.：

Invariant Experiments / 8.：

Invariance, Ergodicity and Mixing / 8.1.：

Invariant Sets and Functions / 8.2.1.：

Invariance as Point Properties / 8.2.2.：

Invariance and Conditional Invariance of [sigma]-Fields / 8.2.3.：

Ergodicity and Mixing / 8.2.4.：

Existence of Invariant Measure / 8.2.5.：

Randomization of the Set of Transformations / 8.2.6.：

Construction and Definition of an Invariant Bayesian Experiment / 8.3.：

Invariance and Reduction / 8.3.2.：

Invariance and Exact Estimability / 8.3.3.：

Invariance in Stochastic Processes / 9.：

Bayesian Stochastic Processes and Representations / 9.1.：

Representation of Experiments / 9.2.1.：

Bayesian Stochastic Processes / 9.2.3.：

Shift and Permutations / 9.2.4.：

Standard Bayesian Stochastic Processes / 9.3.：

Stationary Processes / 9.3.1.：

Exchangeable and i.i.d. Processes / 9.3.2.：

Moving Average Processes / 9.3.3.：

Markovian Stationary Processes / 9.3.4.：

Autoregressive Moving Average Processes / 9.3.5.：

Conditional Stochastic Processes / 9.3.6.：

Shift in Conditional Stochastic Processes / 9.4.1.：

Conditional Shift-Invariance / 9.4.3.：

Bibliography

Author Index

Subject Index

Preface

Notation

Basic Tools and Notation from Probability Theory / 0.：

Introduction / 0.1.：

Measurable Spaces / 0.2.：

[sigma]-Fields / 0.2.1.：

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