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January, 1975 Asymptotic Normality of the Posterior Distribution for Exponential Models
Bradford R. Crain, Ronnie L. Morgan
Ann. Statist. 3(1): 223-227 (January, 1975). DOI: 10.1214/aos/1176343011


Let $f(x)$ be a $\operatorname{pdf}$ of exponential form with respect to the measure $\mu$. Suppose a prior $\operatorname{pdf}$ $\pi$ has been placed on the natural parameter space $\Omega$, where $\pi$ is a density (with respect to $m$-dimensional Lebesgue measure) which is both positive and continuous at $\tau^\ast$, the true but unknown parameter value. Using basic properties of exponential families and certain associated convex functions, it is shown that the posterior pdf tends to the multivariate normal.


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Bradford R. Crain. Ronnie L. Morgan. "Asymptotic Normality of the Posterior Distribution for Exponential Models." Ann. Statist. 3 (1) 223 - 227, January, 1975.


Published: January, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0302.62008
MathSciNet: MR365834
Digital Object Identifier: 10.1214/aos/1176343011

Primary: 62E20
Secondary: 41A60 , 60F05

Keywords: asymptotic normality , Bayesian methods , exponential models , posterior distribution

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 1 • January, 1975
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