On Bayesian adaptation

S. Ghosal; J. Lember; A.W. van der Vaart

doi:10.1023/A:1025856016236

On Bayesian adaptation

S. Ghosal, J. Lember, A.W. van der Vaart

Mathematics

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Abstract

We show that Bayes estimators of an unknown density can adapt to unknown smoothness of the density. We combine prior distributions on each element of a list of log spline density models of different levels of regularity with a prior on the regularity levels to obtain a prior on the union of the models in the list. If the true density of the observations belongs to the model with a given regularity, then the posterior distribution concentrates near this true density at the rate corresponding to this regularity.

Original language	English
Pages (from-to)	165-175
Journal	Acta Applicandae Mathematicae
Volume	79
DOIs	https://doi.org/10.1023/A:1025856016236
Publication status	Published - 2003

Bibliographical note

MR2021886
Proceedings title: Proceedings of the Eighth Vilnius Conference on Probability Theory and Mathematical Statistics, Part II (2002)

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10.1023/A:1025856016236

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On Bayesian adaptation

Abstract

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