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The Wang-Landau algorithm reaches the Flat Histogram criterion in finite time

Jacob, Pierre E.; Ryder, Robin J. (2014), The Wang-Landau algorithm reaches the Flat Histogram criterion in finite time, The Annals of Applied Probability, 24, 1, p. 34-53. http://dx.doi.org/10.1214/12-AAP913

Type
Article accepté pour publication ou publié
Date
2014
Journal name
The Annals of Applied Probability
Volume
24
Number
1
Publisher
Institute of Mathematical Statistics
Pages
34-53
Publication identifier
Metadata
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Author(s)
Jacob, Pierre E. cc

Ryder, Robin J.
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
The Wang-Landau algorithm aims at sampling from a probability distribution, while penalizing some regions of the state space and favouring others. It is widely used, but its convergence properties are still unknown. We show that for some variations of the algorithm, the Wang-Landau algorithm reaches the so-called Flat Histogram criterion in finite time, and that this criterion can be never reached for other variations. The arguments are shown on an simple context -- compact spaces, density functions bounded from both sides-- for the sake of clarity, and could be extended to more general contexts.
Subjects / Keywords
MCMC; Flat Histogram criterion; variations; Wang-Landau algorithm
JEL
C15 - Statistical Simulation Methods: General