A Fully Adaptive Interacting Wang-Landau Algorithm for Automatic Density Exploration

• Activity Number: 661
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Luke Bornn*+
• Companies: University of British Columbia
• Keywords: Monte Carlo ; Wang-Landau ; Multicanonical sampling ; Adaptive Monte Carlo ; Particle Methods ; Parallel

Abstract

In this paper, the authors propose an adaptive density exploration algorithm combining and expanding upon components from various adaptive Markov chain Monte Carlo algorithms. With the Wang-Landau algorithm at its heart, the proposed method adopts several adaptive strategies for improved performance. Firstly, the algorithm is run on interacting parallel chains -- a feature which both decreases computational cost as well as stabilizes the algorithm's flat histogram mechanism. Through interaction, the chains are better able to bias the density to improve exploration. Secondly, a novel adaptive binning strategy is employed, removing the primary obstacle encountered with the Wang-Landau algorithm, namely that of specifying the bins through which to partition the state-space. Thirdly, a standard adaptive proposal is employed to improve the algorithm's ability to explore the already flattened density. The algorithm's performance is studied in several examples.