Importance Weighting in Dynamic and Static Monte Carlo

在本研究中，动态加权被发展为一种动态蒙特卡罗模拟的方法，它能够在存在许多陡能量极小值的情况下有效地对构型空间的相关部分进行采样。该方法依赖于一个额外的动态变量，即重要性权重，以帮助系统克服陡峭的障碍。引入了一种新的非metropolis理论来指导加权采样器的构造。该方法被设计成与对复杂性阶梯进行采样的互补思想相结合。本研究的第二个主题是在顺序重要性抽样中使用拒绝控制。引入这一方法是为了解决静态重要抽样蒙特卡罗方法中权重高度偏斜的问题。这将增强静态蒙特卡罗在高维系统仿真中的实用性。在统计学中，蒙特卡罗是评估和研究似然分布和后验分布的重要计算工具。这种技术在实际贝叶斯推理中的重要性怎么强调也不为过。此外，这项研究所产生的蒙特卡罗理论和方法的进步具有普遍性，对现代科学技术的许多其他领域具有重要意义。在物理科学中，动态蒙特卡罗一直是研究流体、自旋系统、相变和临界现象、材料生长和缺陷以及聚合物行为的不可缺少的工具。在生物学中，蒙特卡罗促进了我们对蛋白质构象的理解，并在遗传和进化分析中发挥了重要作用。在工程中，部分由于其在随机搜索方法中的关键作用，蒙特卡罗在专家系统、网络优化、机器学习和芯片设计等不同领域都很有用。因此，本研究的发现有望为当前从材料研究到蛋白质工程等许多具有战略意义的领域带来可观的利益。

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.