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Bayesian Adaptive Estimation Using a Sieve Prior

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Date
2010
Dewey
Probabilités et mathématiques appliquées
Sujet
Sieve prior; Sobolev
JEL code
C11
Conference name
9th Valencia International Meeting on Bayesian Statistics - 2010 World Meeting of the International Society for Bayesian Analysis
Conference date
06-2010
Conference city
Benidorm
Conference country
Espagne
URI
https://basepub.dauphine.fr/handle/123456789/4639
Collections
  • CEREMADE : Publications
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Author
Arbel, Julyan
Type
Communication / Conférence
Abstract (EN)
We study the Bayes estimation of an infinite dimensional parameter from a Sobolev smoothness class. We propose a family of sieve priors whose resulting Bayes estimators are adaptive optimal, both in posterior concentration rate and in risk convergence for the inherent distance of the model, denoted dn (e.g. the Hellinger distance). This result is applied to several examples, including white noise model, regression function and density model.

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