Elements of Bayesian Statistics

Description

Content: 1.2.1. General Definitions1.2.2. Dominated Experiments 1.2.3. Three Remarks on Regular and Dominated Experiments 1.2.4. A Remark Regarding the Interpretation of Bayesian Experiments 1.2.5. A Remark on Sampling Theory and Bayesian Methods 1.2.6. A Remark Regarding So-called "Improper" Prior Distributions 1.2.7. Families of Bayesian Experiments 1.3. Some Examples of Bayesian Experiments 1.4. Reduction of Bayesian Experiments 1.4.1. Introduction 1.4.2. Marginal Experiments 1.4.3. Conditional Experiment 1.4.4. Complementary Reductions 1.4.5. Dominance in Reduced Experiments 2: Admissible Reductions: Sufficiency and Ancillarity2.1. Introduction 2.2. Conditional Independence 2.2.1. Notation 2.2.2. Definition of Conditional Independence 2.2.3. Null Sets and Completion 2.2.4. Basic Properties of Conditional Independence 2.2.5. Conditional Independence and Densities 2.2.6. Conditional Independence as Point Properties 2.3. Admissible Reductions of an Unreduced Experiment 2.3.1. Introduction 2.3.2. Admissible Reductions on the Sample Space 2.3.3. Admissible Reductions on the Parameter Space 2.3.4. Some Comments on the Definitions 2.3.5. Elementary Properties of Sufficiency and Ancillarity2.3.6. Sufficiency and Ancillarity in a Dominated Experiment 2.3.7. Sampling Theory and Bayesian Methods 2.3.8. A First Result on the Relations between Sufficiency and Ancillarity 3: Admissible Reductions in Reduced Experiments 3.1. Introduction 3.2. Admissible Reduction in Marginal Experiments 3.2.1. Introduction 3.2.2. Basic Concepts 3.2.3. Sufficiency and Ancillarity in Unreduced and in Marginal Experiments 3.2.4. A Remark on "Partial" Sufficiency 3.3. Admissible Reductions in Conditional Experiments 3.3.1. Introduction 3.3.2. Reductions in the Sample Space3.3.3. Reductions in the Parameter Space 3.3.4. Elementary Properties 3.3.5. Relationships between Sufficiency and Ancillarity 3.3.6. Sufficiency and Ancillarity in a Dominated Reduced Experiment 3.4. Jointly Admissible Reductions 3.4.1. Mutual Sufficiency 3.4.2. Mutual Exogeneity 3.4.3. Bayesian Cut 3.4.4. Joint Reductions in a Dominated Experiment 3.4.5. Joint Reductions in a Conditional Experiment 3.4.6. Some Examples 3.5. Comparison of Experiments 3.5.1. Comparison on the Sample Space: Sufficiency