On Bayesian adaptation

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

Research output: Contribution to journalArticleAcademicpeer-review

14 Citations (Scopus)


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 languageEnglish
Pages (from-to)165-175
JournalActa Applicandae Mathematicae
Issue number1-2
Publication statusPublished - 2003


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