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Summary: The Wang-Landau algorithm in general state spaces:
Applications and convergence analysis
Yves F. Atchad´e
and Jun S. Liu
(First version Nov. 2004; Revised Feb. 2007, Aug. 2008)
Abstract: The Wang-Landau algorithm ([21]) is a recent Monte Carlo method that has
generated much interest in the Physics literature due to some spectacular simulation per-
formances. 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 con-
ditions. We have also shown by simulations the potential advantage of the WL algorithm
for problems in the Bayesian inference.
AMS 2000 subject classifications: Primary 60C05, 60J27, 60J35, 65C40.
Keywords and phrases: Monte Carlo methods, Wang-Landau algorithm, Multicanonical
sampling, Trans-dimensional MCMC, Adaptive MCMC, Geometric ergodicity, Stochastic
approximation.
1. Introduction
Although the idea of Monte Carlo computation has been around for more than a century, its
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