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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, May 23, 2000}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Aad van der Vaart}
\centerline{\sl Free University of Amsterdam}
\centerline{\sl currently Miller Professor, UC Berkeley}
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\centerline{\bf Rates of convergence of posterior distributions}
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We consider posterior distributions relative to priors on
infinite-dimensional models. After presenting some general results on the
rate of convergence in Hellinger, $L_1$ or $L_2$-distances, we focus on some
examples. These include mixtures of Gaussian location and scale models,
where the prior is constructed by putting Dirichlet process priors on the
joint (mixing) distribution of the location and scale parameters. We finish
with some results on adaptative estimation using Bayesian model selection.

(Based on joint work with Subhashis Ghosal.)

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