Universiteit Utrecht

Department of Mathematics


Bayesian Density Estimation with Location-Scale Mixtures



Willem Kruijer
(VU)

12 June 2007

In this talk we consider finite location-scale mixtures as a model for Bayesian density estimation, and discuss asymptotic properties. Ghosal and Van der Vaart (2001,2007) obtained convergence rates for normal mixtures with Dirichlet priors. In this talk their results will be extended to other priors, the kernel being of the form exp{-|x|^p} . It is assumed that the underlying density is twice continuously differentiable and has exponential tails. General conditions on the prior will be formulated, under which the posterior converges to the true density at a near optimal rate. Examples of priors that satisfy these conditions include Polya tree priors (on the weights) and Poisson process priors (on the locations). Some of the results can be extended to Cauchy mixtures, in which case the rate becomes suboptimal.


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Charlene Kalle