Generalized and hybrid Metropolis-Hastings overdamped Langevin algorithms - Département de mathématiques appliquées Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2017

Generalized and hybrid Metropolis-Hastings overdamped Langevin algorithms

Résumé

It has been shown that the nonreversible overdamped Langevin dynamics enjoy better convergence properties in terms of spectral gap and asymptotic variance than the reversible one. In this article we propose a variance reduction method for the Metropolis-Hastings Adjusted Langevin Algorithm (MALA) that makes use of the good behaviour of the these nonreversible dynamics. It consists in constructing a nonreversible Markov chain (with respect to the target invariant measure) by using a Generalized Metropolis-Hastings adjustment on a lifted state space. We present two variations of this method and we discuss the importance of a well-chosen proposal distribution in terms of average rejection probability. We conclude with numerical experimentations to compare our algorithms with the MALA, and show variance reduction of several orders of magnitude in some favourable toy cases.
Fichier principal
Vignette du fichier
main.pdf (591.5 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01440499 , version 1 (19-01-2017)

Identifiants

Citer

Romain Poncet. Generalized and hybrid Metropolis-Hastings overdamped Langevin algorithms. 2017. ⟨hal-01440499⟩
244 Consultations
260 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More