Abstract

This article provides a first theoretical analysis on a new Monte Carlo approach, the dynamic weighting, proposed recently by Wong and Liang. In dynamic weighting, 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 behaviors 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 the neural network training and the Ising model simulations. Keywords: Gibbs Sampling; Importance Sampling; Ising Model, Metropolis algorithm, Neural Network, Renewal Theory, Simulated Annealing, Simulated Tempering, 1 Jun S. Liu is Assistant Professor, Department of Statisti...

Citations