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

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Date
2014
Dewey
Probabilités et mathématiques appliquées
Sujet
MCMC; Flat Histogram criterion; variations; Wang-Landau algorithm
JEL code
C15
Journal issue
The Annals of Applied Probability
Volume
24
Number
1
Publication date
2014
Article pages
34-53
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/12-AAP913
URI
https://basepub.dauphine.fr/handle/123456789/7267
Collections
  • CEREMADE : Publications
Metadata
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Author
Jacob, Pierre E.
Ryder, Robin J.
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
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.

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