✦ LIBER ✦

Asymptotic Normality of Posterior Distributions for Exponential Families when the Number of Parameters Tends to Infinity

✍ Scribed by Subhashis Ghosal

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 172 KB
Volume: 74
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.1999.1874

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✦ Synopsis

We study consistency and asymptotic normality of posterior distributions of the natural parameter for an exponential family when the dimension of the parameter grows with the sample size. Under certain growth restrictions on the dimension, we show that the posterior distributions concentrate in neighbourhoods of the true parameter and can be approximated by an appropriate normal distribution.