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.
Bayesian asymptotics with misspecified models
DE BLASI, Pierpaolo;
2013
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.
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