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Bayesian Theory and Applications$
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Paul Damien, Petros Dellaportas, Nicholas G. Polson, and David A. Stephens

Print publication date: 2013

Print ISBN-13: 9780199695607

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199695607.001.0001

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Proper and non-informative conjugate priors for exponential family models

Proper and non-informative conjugate priors for exponential family models

Chapter:
(p.395) 19 Proper and non-informative conjugate priors for exponential family models
Source:
Bayesian Theory and Applications
Author(s):

E GUTIéRREZ - PEñA

M MENDOZA

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199695607.003.0019

This chapter demonstrates that, in the context of exponential families, under certain conditions, Jeffreys' prior and other non-informative priors — including some forms of ‘unbiased’ priors — can be obtained as suitable limits of conjugate distributions. Moreover, there exists an interesting duality between unbiased estimators and optimal Bayes estimators that minimize expected risk. The chapter is organized as follows. Section 19.2 briefly reviews some basic concepts concerning exponential families and information theory. Section 19.3 discusses Bayesian inference for exponential families based both on proper and certain non-informative, improper conjugate priors. Section 19.4 looks at more general versions of these latter priors and discusses an interesting unbiasedness property of maximum likelihood estimators. Section 19.5 contains some concluding remarks.

Keywords:   exponential families, Jeffreys' prior, information theory, Bayesian inference, maximum likelihood estimators

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