An Adaptive Interacting Wang-Landau Algorithm for Automatic Density Exploration

TL;DR

This paper introduces an adaptive, interacting Wang-Landau algorithm designed for automatic density exploration, enhancing mode-jumping, convergence, and efficiency in complex Bayesian and spatial models.

Contribution

It presents a novel adaptive algorithm combining Wang-Landau with interacting chains for improved density exploration in Monte Carlo methods.

Findings

Enhanced convergence with interacting chains

Effective mode-jumping in multimodal densities

Overcomes high correlations in spatial models

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 which we feel deserves much further attention. Towards this aim, this paper 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 which both decreases computational cost as well as stabilizes the algorithm, improving its ability to explore the density. Performance is studied in several applications. Through a Bayesian variable selection example, the authors demonstrate the convergence gains obtained with interacting chains. The ability of the algorithm's adaptive proposal to induce mode-jumping is illustrated through a trimodal density and a Bayesian mixture modeling application. Lastly, through a 2D Ising model, the authors demonstrate the ability of the algorithm to overcome the high correlations encountered in spatial models.