Open Access
Translator Disclaimer
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

Abstract

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.

Citation

Download Citation

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

Information

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

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

Subjects:
Primary: 62E20
Secondary: 41A60 , 60F05

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

Rights: Copyright © 1975 Institute of Mathematical Statistics

JOURNAL ARTICLE
5 PAGES


SHARE
Vol.3 • No. 1 • January, 1975
Back to Top