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Posterior concentration rates for infinite dimensional exponential families

Rivoirard, Vincent; Rousseau, Judith (2012), Posterior concentration rates for infinite dimensional exponential families, Bayesian Analysis, 7, 2, p. 311-334. http://dx.doi.org/10.1214/12-BA710

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00634432/fr/
Date
2012
Journal name
Bayesian Analysis
Volume
7
Number
2
Publisher
International Society for Bayesian Analysis
Pages
311-334
Publication identifier
Metadata
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Author(s)
Rivoirard, Vincent
Rousseau, Judith
Abstract (EN)
In this paper we derive adaptive non-parametric rates of concentration of the posterior distributions for the density model on the class of Sobolev and Besov spaces. For this purpose, we build prior models based on wavelet or Fourier expansions of the logarithm of the density. The prior models are not necessarily Gaussian
Subjects / Keywords
Sobolev balls; Besov balls; Bayesian non-parametric; rates of convergence; adaptive estimation; wavelets; Fourier Bases
JEL
C11 - Bayesian Analysis: General