A theory for dynamic weighting in Monte Carlo computation

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