Bayesian Nonparametric Inference of decreasing densities - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2010

Bayesian Nonparametric Inference of decreasing densities


Abstract In this paper we discuss consistency of the posterior distribution in cases where the Kullback-Leibler condition is not verified. This condition is stated as : for all $\epsilon > 0$ the prior probability of sets in the form $\{f ; KL(f0 , f ) \leq \epsilon\}$ where KL(f0 , f ) denotes the Kullback-Leibler divergence between the true density f0 of the observations and the density f , is positive. This condi- tion is in almost cases required to lead to weak consistency of the posterior distribution, and thus to lead also to strong consistency. However it is not a necessary condition. We therefore present a new condition to replace the Kullback-Leibler condition, which is usefull in cases such as the estimation of decreasing densities. We then study some specific families of priors adapted to the estimation of decreasing densities and provide posterior concentration rate for these priors, which is the same rate a the convergence rate of the maximum likelihood estimator. Some simulation results are provided. Keywords: Nonparametric Bayesian inference, Consistency, entropy, Kullback Leibler, k-monotone density, kernel mixture.
Fichier principal
Vignette du fichier
p231.pdf (24.46 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

inria-00494692 , version 1 (24-06-2010)


  • HAL Id : inria-00494692 , version 1


Soleiman Khazaei, Judith Rousseau. Bayesian Nonparametric Inference of decreasing densities. 42èmes Journées de Statistique, 2010, Marseille, France. pp.USB-key. ⟨inria-00494692⟩
192 View
66 Download


Gmail Facebook X LinkedIn More