Importance Weighting in Dynamic and Static Monte Carlo

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9703918 Wong In this research, dynamic weighting is developed as a method for dynamic Monte Carlo simulation that has the capability to efficiently sample relevant parts of the configuration space in the presence of many steep energy minima. This method relies on an additional dynamic variable, namely the importance weight, to help the system overcome steep barriers. A new, non-Metropolis theory is introduced to guide the construction of such weighted samplers. The method is designed to work in combination with the complementary idea of sampling a complexity ladder. A second topic studied in this research is the use of rejection control in sequential importance sampling. This is introduced in order to cope with difficulties of having highly skewed weights in static importance sampling Monte Carlo. It will enhance the usefulness of static Monte Carlo in the simulation of high dimensional systems. In statistics, Monte Carlo is an essential computational tool in the evaluation and study of likelihoods and posterior distributions. The importance of this technique in practical Bayesian inference cannot be overstated. Furthermore, the advances in Monte Carlo theory and method resulting from this investigation are of a general nature and have significance to many other areas in modern science and technology. In physical sciences, dynamic Monte Carlo has long been an indispensible tool in the study of fluids, spin systems, phase transitions and critical phenomena, material growth and defect, and the behavior of polymers. In biology, Monte Carlo advances our understanding of protein conformations, and plays an important role in genetic and evolutionary analysis. In engineering, partly through its pivotal role in stochastic search methods, Monte Carlo is useful in such diverse areas as expert system, network optimization, machine learning and chip design. Therefore, the findings of this research are expected to bring considerable benefit to many current areas of strategic importance rang ing from material research to protein engineering.