A Theory for Dynamic Weighting in Monte Carlo Computation

Abstract

This article provides a first theoretical analysis of a new Monte Carlo approach, the dynamic weighting algorithm , proposed recently by Wong and Liang. In dynamic weighting Monte Carlo, one augments the original state space of interest by a weighting factor, which allows the resulting Markov chain to move more freely and to escape from local modes. It uses a new invariance principle to guide the construction of transition rules. We analyze the behavior of the weights resulting from such a process and provide detailed recommendations on how to use these weights properly. Our recommendations are supported by a renewal theory-type analysis. Our theoretical investigations are further demonstrated by a simulation study and applications in neural network training and Ising model simulations.