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Journal Articles Journal of Computational and Graphical Statistics Year : 2013

An Adaptive Interacting Wang-Landau Algorithm for Automatic Density Exploration

Abstract

While statisticians are well-accustomed to performing exploratory analysis in the modeling stage of an analysis, the notion of conducting preliminary general-purpose exploratory analysis in the Monte Carlo stage (or more generally, the model-fitting stage) of an analysis is an area that we feel deserves much further attention. Toward this aim, this article proposes a general-purpose algorithm for automatic density exploration. The proposed exploration algorithm combines and expands upon components from various adaptive Markov chain Monte Carlo methods, with the Wang-Landau algorithm at its heart. Additionally, the algorithm is run on interacting parallel chains--a feature that both decreases computational cost as well as stabilizes the algorithm, improving its ability to explore the density. Performance of this new parallel adaptive Wang-Landau algorithm is studied in several applications. Through a Bayesian variable selection example, we demonstrate the convergence gains obtained with interacting chains. The ability of the algorithm's adaptive proposal to induce mode-jumping is illustrated through a Bayesian mixture modeling application. Last, through a two-dimensional Ising model, the authors demonstrate the ability of the algorithm to overcome the high correlations encountered in spatial models. Supplemental materials are available online.

Dates and versions

hal-00932238 , version 1 (16-01-2014)

Identifiers

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Luke Bornn, Pierre E. Jacob, Pierre del Moral, Arnaud Doucet. An Adaptive Interacting Wang-Landau Algorithm for Automatic Density Exploration. Journal of Computational and Graphical Statistics, 2013, 22 (3), ⟨10.1080/10618600.2012.723569⟩. ⟨hal-00932238⟩
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