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Bayesian Statistics 9$
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José M. Bernardo, M. J. Bayarri, James O. Berger, A. P. Dawid, David Heckerman, Adrian F. M. Smith, and Mike West

Print publication date: 2011

Print ISBN-13: 9780199694587

Published to Oxford Scholarship Online: January 2012

DOI: 10.1093/acprof:oso/9780199694587.001.0001

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Integrated Objective Bayesian Estimation and Hypothesis Testing

Integrated Objective Bayesian Estimation and Hypothesis Testing

(p.1) Integrated Objective Bayesian Estimation and Hypothesis Testing
Bayesian Statistics 9

José M. Bernardo

Oxford University Press

The complete final product of Bayesian inference is the posterior distribution of the quantity of interest. Important inference summaries include point estimation, region estimation and precise hypotheses testing. Those summaries may appropriately be described as the solution to specific decision problems which depend on the particular loss function chosen. The use of a continuous loss function leads to an integrated set of solutions where the same prior distribution may be used throughout. Objective Bayesian methods are those which use a prior distribution which only depends on the assumed model and the quantity of interest. As a consequence, objective Bayesian methods produce results which only depend on the assumed model and the data obtained. The combined use of intrinsic discrepancy, an invariant information‐based loss function, and appropriately defined reference priors, provides an integrated objective Bayesian solution to both estimation and hypothesis testing problems. The ideas are illustrated with a large collection of non‐trivial examples.

Keywords:   Foundations, Decision Theory, Kullback–Leibler Divergence, Intrinsic Discrepancy, Reference Analysis, Reference Priors, Point Estimation, Interval Estimation, Region Estimation, Precise Hypothesis Testing, Hardy–Weinberg Equilibrium, Contingency Tables

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