CAREER: Efficient Monte Carlo Methods in Engineering and Science: From Coarse Analysis to Refined Estimators

职业：工程和科学中的高效蒙特卡罗方法：从粗略分析到精细估算器

• 批准号: 0846816
• 负责人: Jose Blanchet
• 金额: $ 40万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0846816&HistoricalAwards=false
• 关键词: CAREER; Efficient; Monte; Carlo; Methods

The research objective of this Faculty Early Career Development (CAREER) project is to investigate and develop a framework that exploits asymptotic analysis, expressed at a coarse scale, to systematically generate efficient rare-event simulation algorithms for complex stochastic systems, which must necessarily be implemented at a fine scale. The objective is to study five types of environments that exhibit stylized features that have not been well studied in rare-event simulation, namely, a) Stochastic recursions with heavy-tails (which are used to model insurance risk and reservoir processes), b) Heavy-tailed queues (which arise in database and networking applications), c) Counting problems and inference for combinatorial structures (arising in sociology and biology), d) Location of objects immersed in a random medium (with particular emphasis on military applications where one needs to find targets that have eluded detection for long time), and e) Random fields (which arise in settings such as oceanography, environmental studies and medical imaging). The strategy consists in connecting large deviations analysis with algorithmic design of efficient simulation estimators. A key tool that we exploit in the design and performance analysis of our algorithms is a systematic use of Lyapunov bounds for Markov chains, combined with parametric families of importance sampling distributions. Events such as environmental or natural disasters, major market crashes, pension and insurance breakdowns and terrorist attacks are rare but consequential. If successful, the proposed research program will provide efficient computational tools for risk assessment of such events which exhibit features such as heavy-tails, complex dependence and incorporation of combinatorial objects. Efficient evaluation of rare-event probabilities can provide decision makers with key quantitative policy assessment metrics and accompanying insights. Examples include computing the probability that a target is able to evade a set of detectors as well as its conditional most likely location, and assessing ruin probabilities for purposes of sizing the capital reserve of insurance and financial companies.

该教师早期职业发展（CAREER）项目的研究目标是研究和开发一个框架，该框架利用以粗尺度表示的渐近分析，系统地为复杂随机系统生成有效的罕见事件模拟算法，该算法必须被实现在一个精细的尺度上。目标是研究五种类型的环境，这些环境表现出在罕见事件模拟中尚未得到充分研究的程式化特征，即：a）具有重尾的随机递归（用于对保险风险和水库过程进行建模），b）重尾队列（出现在数据库和网络应用中），c）组合结构的计数问题和推理（出现在社会学和生物学中），d）沉浸在随机介质中的物体的位置（特别强调军事应用）需要找到长时间躲避检测的目标），以及 e) 随机场（出现在海洋学、环境研究和医学成像等环境中）。该策略包括将大偏差分析与高效模拟估计器的算法设计联系起来。我们在算法设计和性能分析中利用的一个关键工具是系统地使用马尔可夫链的李亚普诺夫界限，并结合重要采样分布的参数族。 环境或自然灾害、重大市场崩盘、养老金和保险崩溃以及恐怖袭击等事件虽然罕见，但后果却很严重。如果成功，拟议的研究计划将为此类事件的风险评估提供有效的计算工具，这些事件具有重尾、复杂依赖性和组合对象合并等特征。对罕见事件概率的有效评估可以为决策者提供关键的定量政策评估指标和相关见解。示例包括计算目标能够躲避一组探测器的概率及其有条件的最可能位置，以及评估破坏概率以调整保险和金融公司的资本储备规模。