HAL : hal-00019174, version 3

arXiv : math.ST/0605263

Fiche détaillée

Récupérer au format BibTeX - EndNote - TEI - RefWorks -

Versions disponibles :

v1 (17-02-2006)

v2 (10-05-2006)

v3 (10-04-2007)

How to compare MCMC simulation strategies?

Didier Chauveau 1, Pierre Vandekerkhove 2

(04/2007)

In MCMC methods, such as the Metropolis-Hastings (MH) algorithm, the Gibbs sampler, or recent adaptive methods, many different strategies can be proposed, often associated in practice to unknown rates of convergence. In this paper we propose a simulation-based methodology to compare these rates of convergence, grounded on an entropy criterion computed from parallel (i.i.d.) simulated Markov chains coming from each candidate strategy. Our criterion determines the most efficient strategy among the candidates. Theoretically, we give for the MH algorithm general conditions under which its successive densities satisfy adequate smoothness and tail properties, so that this entropy criterion can be estimated consistently using kernel density estimate and Monte Carlo integration. Simulated and actual examples in moderate dimensions are provided to illustrate this approach.

1 :	Mathématiques et Applications, Physique Mathématique d'Orléans (MAPMO)
	CNRS : UMR6628 – Université d'Orléans
2 :	Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA)
	CNRS : UMR8050 – Université Paris XII - Paris Est Créteil Val-de-Marne – Université Paris XII - Paris Est Créteil Val-de-Marne

Domaine

:

Mathématiques/Statistiques

Mots Clés : Bayesian model – Entropy – Kullback divergence – Markov Chain Monte Carlo – Metropolis-Hastings algorithm – nonparametric statistic – proposal distribution

hal-00019174, version 3

http://hal.archives-ouvertes.fr/hal-00019174

oai:hal.archives-ouvertes.fr:hal-00019174

Contributeur : Didier Chauveau <>

Soumis le : Mardi 10 Avril 2007, 16:33:22

Dernière modification le : Mardi 10 Avril 2007, 16:35:29