Convergence rates for posterior distributions and adaptive estimation

Details Convergence rates for posterior distributions and adaptive estimation Convergence rates for posterior distributions and adaptive estimation

2004-10-05

arxiv.org/abs/math/0410087v1

Annals of Statistics 2004, Vol. 32, No. 4, 1556-1593

Mathematics

Statistics Theory

Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat

Scientific paper

10.1214/009053604000000490

The goal of this paper is to provide theorems on convergence rates of posterior distributions that can be applied to obtain good convergence rates in the context of density estimation as well as regression. We show how to choose priors so that the posterior distributions converge at the optimal rate without prior knowledge of the degree of smoothness of the density function or the regression function to be estimated.

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