Langevin diffusions and the Metropolis-adjusted Langevin algorithm

2013/09/11 by Tatiana Xifara, Chris Sherlock, Samuel Livingstone +2 · 2 citations
Mathematics · #stat.ME #math.ST #stat.TH

paper · pdf · doi:10.1016/j.spl.2014.04.002

published as Statistics & Probability Letters. Volume 91, August 2014, pages 14-19

arxiv created 2013/09/11 · arxiv updated 2014/08/15

Abstract

We provide a clarification of the description of Langevin diffusions on Riemannian manifolds and of the measure underlying the invariant density. As a result we propose a new position-dependent Metropolis-adjusted Langevin algorithm (MALA) based upon a Langevin diffusion in ℝ^d which has the required invariant density with respect to Lebesgue measure. We show that our diffusion and the diffusion upon which a previously-proposed position-dependent MALA is based are equivalent in some cases but are distinct in general. A simulation study illustrates the gain in efficiency provided by the new position-dependent MALA.

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