On Bayesian adaptation

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

    Research output: Contribution to journalArticleAcademicpeer-review

    14 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)165-175
    JournalActa Applicandae Mathematicae
    Volume79
    Issue number1-2
    DOIs
    Publication statusPublished - 2003

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