Atchadé, Yves F.Liu, Jun2015-03-132010Atchadé, Yves F., and Jun S. Liu. 2010. "The Wang-Landau algorithm in general state spaces: applications and convergence analysis." Statistica Sinica 20 (1): 209-233.1017-0405http://nrs.harvard.edu/urn-3:HUL.InstRepos:14169382The 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.en-USAdaptive MCMCgeometric ergodicityMonte Carlo methodsmulticanonical samplingstochastic approximationtrans-dimensional MCMCWang-Landau algorithmJournal Article2015-03-13