Sticky proposal densities for adaptive MCMC methods

Abstract

Monte Carlo (MC) methods are commonly used in Bayesian signal processing to address complex inference problems. The performance of any MC scheme depends on the similarity between the proposal (chosen by the user) and the target (which depends on the problem). In order to address this issue, many adaptive MC approaches have been developed to construct the proposal density iteratively. In this paper, we focus on adaptive Markov chain MC (MCMC) algorithms, introducing a novel class of adaptive proposal functions that progressively stick to the target. This proposed class of sticky MCMC methods converge very fast to the target, thus being able to generate virtually independent samples after a few iterations. Numerical simulations illustrate the excellent performance of the sticky proposals when compared to other adaptive and non-adaptive schemes.