Smoothed Langevin proposals in Metropolis-Hastings algorithms

The Metropolis Adjusted Langevin Algorithm (MALA) samples from complex multivariate densities π. The proposal density is based on a discretized version of a Langevin diffusion, and is well defined only for continuously differentiable densities π. We propose a modified MALA algorithm when this condition is not fulfilled or when π has very rapid variations. The algorithm is illustrated on the Strauss model, for which two different classes of smoothing are proposed. In these examples smoothing gives advantages in terms of reduced asymptotic variance.