Bayesian optimal adaptive estimation using a sieve prior

Details Bayesian optimal adaptive estimation using a sieve prior Bayesian optimal adaptive estimation using a sieve prior

2012-04-11

arxiv.org/abs/1204.2392v1

Mathematics

Statistics Theory

26 pages, 2 figures

Scientific paper

We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure, and rate adaptation when the parameter space is, e.g., a Sobolev class. The conditions employed, although standard in the literature, are combined in a novel way. The results are applied to density, regression, nonlinear autoregression and Gaussian white noise models. In the latter we have also considered a loss function which is different from the usual L2 norm, namely the pointwise loss. In this case it is possible to prove that the adaptive Bayesian approach for the L2 loss is strongly suboptimal and we provide a lower bound on the rate.

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