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Statistica Sinica 20 (2010), 209-233





THE WANG-LANDAU ALGORITHM

IN GENERAL STATE SPACES:

APPLICATIONS AND CONVERGENCE ANALYSIS


Yves F. Atchadé and Jun S. Liu


University of Michigan and Harvard University


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.



Key words and phrases: Adaptive MCMC, geometric ergodicity, Monte Carlo methods, multicanonical sampling, stochastic approximation, trans-dimensional MCMC, Wang-Landau algorithm.

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