Statistica Sinica 23 (2013), 169-187

doi:http://dx.doi.org/10.5705/ss.2010.239

BAYESIAN ASYMPTOTICS WITH MISSPECIFIED MODELS

Pierpaolo De Blasi$^{1,2}$ and Stephen G. Walker$^3$

$^1$University of Torino, $^2$Collegio Carlo Alberto and $^3$University of Kent

Abstract: In this paper, we study the asymptotic properties of a sequence of posterior distributions based on an independent and identically distributed sample and when the Bayesian model is misspecified. We find a sufficient condition on the prior for the posterior to accumulate around the densities in the model closest in the Kullback-Leibler sense to the true density function. Examples are presented.

Key words and phrases: Asymptotics, consistency, misspecified model.