Large Deviation Theory Applications to Importance Sampling Monte Carlo Techniques

大偏差理论在重要采样蒙特卡罗技术中的应用

• 批准号: 9104823
• 负责人: James Bucklew
• 金额: $ 11.47万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-15 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9104823&HistoricalAwards=false
• 关键词: Large; Deviation; Theory; Applications; Importance

This is an investigation of a new importance sampling technique called twisted simulation. In the i.i.d. case it corresponds to simulating the events of interest via an exponentially shifted version of the direct simulation probability measures. In the finite dimensional Markov chains of i.i.d. random variables the method is optimal over a large class of importance sampling distributions in the sense of minimizing the asymptotic variance of the estimates. The work may be extended to more useful probability models, in particular Markov additive processes and multidimensional event sets. The theoretical extensions require different analysis techniques than have been used previously. The techniques and tools involved will be sophisticated and involved, bust due to the conjectured optimality of the method, the effort expended on these theoretical investigations should have substantial payoff in applications. The methods promise to provide a rigorous structure for the pursuit of the study of simulation of systems with memory.

本文研究了一种新的重要采样技术——扭曲模拟。在i.i.d情况下，它对应于通过直接模拟概率度量的指数移位版本来模拟感兴趣的事件。在i.i.d随机变量的有限维马尔可夫链中，从最小化估计的渐近方差的意义上说，该方法在一大类重要抽样分布上是最优的。这项工作可以扩展到更有用的概率模型，特别是马尔可夫加性过程和多维事件集。理论扩展需要不同于以前使用的分析技术。所涉及的技术和工具将是复杂和复杂的，但由于该方法的推测最优性，在这些理论研究上所付出的努力应该在应用中有实质性的回报。这些方法有望为具有内存的系统的仿真研究提供一个严格的结构。