A shrinkage-thresholding Metropolis adjusted Langevin algorithm for Bayesian variable selection

Amandine Schreck (1) , Gersende Fort (1) , Sylvain Le Corff (2) , Eric Moulines (1)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 Département de Mathématiques-Université de Paris XI

This paper introduces a new Markov Chain Monte Carlo method for Bayesian variable selection in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines a Metropolis Adjusted Langevin (MALA) step to propose local moves associated with a shrinkage-thresholding step allowing to propose new models. The geometric ergodicity of this new trans-dimensional Markov Chain Monte Carlo sampler is established. An extensive numerical experiment, on simulated and real data, is presented to illustrate the performance of the proposed algorithm in comparison with some more classical trans-dimensional algorithms.

Mots clés: Proximal operators; Markov chain Monte Carlo; Bayesian variable selection

Domaines: Modélisation et simulation; Statistiques [math.ST]; Théorie [stat.TH]

Amandine Schreck, Gersende Fort, Sylvain Le Corff, Eric Moulines. A shrinkage-thresholding Metropolis adjusted Langevin algorithm for Bayesian variable selection. 2015. ⟨hal-00921130v3⟩