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Remarks on consistency of posterior distributions

Taeryon Choi and R. V. Ramamoorthi

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In recent years, the literature in the area of Bayesian asymptotics has been rapidly growing. It is increasingly important to understand the concept of posterior consistency and validate specific Bayesian methods, in terms of consistency of posterior distributions. In this paper, we build up some conceptual issues in consistency of posterior distributions, and discuss panoramic views of them by comparing various approaches to posterior consistency that have been investigated in the literature. In addition, we provide interesting results on posterior consistency that deal with non-exponential consistency, improper priors and non i.i.d. (independent but not identically distributed) observations. We describe a few examples for illustrative purposes.

Chapter information

Bertrand Clarke and Subhashis Ghosal, eds., Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 170-186

First available in Project Euclid: 28 April 2008

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Mathematical Reviews number (MathSciNet)

Primary: 62G20: Asymptotic properties
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures 62F15: Bayesian inference

affinity Doob’s theorem exponential consistency posterior distribution strongly separated

Copyright © 2008, Institute of Mathematical Statistics


Choi, Taeryon; Ramamoorthi, R. V. Remarks on consistency of posterior distributions. Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh, 170--186, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/074921708000000138.

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