Open Access
VOL. 3 | 2008 Remarks on consistency of posterior distributions
Taeryon Choi, R. V. Ramamoorthi

Editor(s) Bertrand Clarke, Subhashis Ghosal

Inst. Math. Stat. (IMS) Collect., 2008: 170-186 (2008) DOI: 10.1214/074921708000000138


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.


Published: 1 January 2008
First available in Project Euclid: 28 April 2008

MathSciNet: MR2459224

Digital Object Identifier: 10.1214/074921708000000138

Primary: 62G20
Secondary: 62C10 , 62F15

Keywords: affinity , Doob’s theorem , exponential consistency , posterior distribution , strongly separated

Rights: Copyright © 2008, Institute of Mathematical Statistics

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