2006/07/01 by B. J. K. Kleijn, A. W. van der Vaart · 1 citation
Mathematics · #math.ST #stat.TH #msc:62G07 #msc:62G08 #msc:62G20 #msc:62F05 #msc:62F15
paper · pdf · doi:10.1214/009053606000000029
published as Annals of Statistics 2006, Vol. 34, No. 2, 837-877 · Published at http://dx.doi.org/10.1214/009053606000000029 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
arxiv created 2006/07/01 · arxiv updated 2009/12/01
We 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.