Misspecification in infinite-dimensional Bayesian statistics
2006; Institute of Mathematical Statistics; Volume: 34; Issue: 2 Linguagem: Inglês
10.1214/009053606000000029
ISSN2168-8966
AutoresB. J. K. Kleijn, Aad van der Vaart,
Tópico(s)Statistical Methods and Bayesian Inference
ResumoWe consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution P0, which may not be in the support of the prior, we show that the posterior concentrates its mass near the points in the support of the prior that minimize the Kullback–Leibler divergence with respect to P0. An entropy condition and a prior-mass condition determine the rate of convergence. The method is applied to several examples, with special interest for infinite-dimensional models. These include Gaussian mixtures, nonparametric regression and parametric models.
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