Bayesian Analysis

Posterior Concentration Rates for Infinite Dimensional Exponential Families

Vincent Rivoirard and Judith Rousseau

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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.

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Bayesian Anal., Volume 7, Number 2 (2012), 311-334.

First available in Project Euclid: 16 June 2012

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Bayesian non-parametric rates of convergence adaptive estimation wavelets and Fourier Bases Sobolev and Besov balls


Rivoirard, Vincent; Rousseau, Judith. Posterior Concentration Rates for Infinite Dimensional Exponential Families. Bayesian Anal. 7 (2012), no. 2, 311--334. doi:10.1214/12-BA710.

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