Bayesian Optimal Adaptive Estimation Using a Sieve Prior
Arbel, Julyan; Gayraud, Ghislaine; Rousseau, Judith (2013), Bayesian Optimal Adaptive Estimation Using a Sieve Prior, Scandinavian Journal of Statistics, 40, 3, p. 549-570. http://dx.doi.org/10.1002/sjos.12002
TypeArticle accepté pour publication ou publié
Journal nameScandinavian Journal of Statistics
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Abstract (EN)We derive rates of contraction of posterior distributions on non-parametric models resulting from sieve priors. The aim of the study was to provide general conditions to get posterior rates when the parameter space has a general structure, and rate adaptation when the parameter is, for example, a Sobolev class. The conditions employed, although standard in the literature, are combined in a different 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.
Subjects / Keywordsadaptation; minimax criteria; non-parametric models; rate of contraction; sieve prior; white noise model
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Bayesian nonparametric dependent model for partially replicated data: The influence of fuel spills on species diversity Arbel, Julyan; Mengersen, Kerrie; Rousseau, Judith (2016) Article accepté pour publication ou publié