The Wang-Landau algorithm in general state spaces: applications and convergence analysis

Abstract

The Wang-Landau algorithm (Wang and Landau (2001)) is a recent Monte Carlo method that has generated much interest in the Physics literature due to some spectacular simulation performances. The objective of this paper is two-fold. First, we show that the algorithm can be naturally extended to more general state spaces and used to improve on Markov Chain Monte Carlo schemes of more interest in Statistics. In a second part, we study asymptotic behaviors of the algorithm. We show that with an appropriate choice of the step-size, the algorithm is consistent and a strong law of large numbers holds under some fairly mild conditions. We have also shown by simulations the potential advantage of the WL algorithm for problems in Bayesian inference.