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Content
General Definitions
Dominated Experiments
Three Remarks on Regular and Dominated Experiments
A Remark Regarding the Interpretation of Bayesian Experiments
A Remark on Sampling Theory and Bayesian Methods
A Remark Regarding So-called "Improper" Prior Distributions
Families of Bayesian Experiments
Some Examples of Bayesian Experiments
Reduction of Bayesian Experiments
Introduction
Marginal Experiments
Conditional Experiment
Complementary Reductions
Dominance in Reduced Experiments
Admissible Reductions Sufficiency and Ancillarity
Introduction
Conditional Independence
Notation
Definition of Conditional Independence
Null Sets and Completion
Basic Properties of Conditional Independence
Conditional Independence and Densities
Conditional Independence as Point Properties
Admissible Reductions of an Unreduced Experiment
Introduction
Admissible Reductions on the Sample Space
Admissible Reductions on the Parameter Space
Some Comments on the Definitions
Elementary Properties of Sufficiency and Ancillarity
Sufficiency and Ancillarity in a Dominated Experiment
Sampling Theory and Bayesian Methods
A First Result on the Relations between Sufficiency and Ancillarity
Admissible Reductions in Reduced Experiments
Introduction
Admissible Reduction in Marginal Experiments
Introduction
Basic Concepts
Sufficiency and Ancillarity in Unreduced and in Marginal Experiments
A Remark on "Partial" Sufficiency
Admissible Reductions in Conditional Experiments
Introduction
Reductions in the Sample Space
Reductions in the Parameter Space
Elementary Properties
Relationships between Sufficiency and Ancillarity
Sufficiency and Ancillarity in a Dominated Reduced Experiment
Jointly Admissible Reductions
Mutual Sufficiency
Mutual Exogeneity
Bayesian Cut
Joint Reductions in a Dominated Experiment
Joint Reductions in a Conditional Experiment
Some Examples
Comparison of Experiments
Comparison on the Sample Space Sufficiency