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 Department of Statistics [Warwick]

This paper introduces a new Markov Chain Monte Carlo method to perform Bayesian variable selection in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines (i) a Metropolis adjusted Langevin step to propose local moves associated with the differentiable part of the target density with (ii) a shrinkage-thresholding step based on the non-differentiable part of the target density which provides sparse solutions such that small components are shrunk toward zero. This allows to sample from distributions on spaces with different dimensions by actually setting some components to zero. The performances of this new procedure are illustrated with both simulated and real data sets. The geometric ergodicity of this new transdimensional Markov Chain Monte Carlo sampler is also established.

Mots clés: Markov chain Monte Carlo; proximal operators; 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. 2013. ⟨hal-00921130v1⟩