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（职业）项目的研究目标是调查和开发一个框架，该框架利用了以粗略表达的渐近分析，以系统地生成有效的复杂随机系统的有效的稀有事实模拟算法，必须以精细的规模实施。 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）浸入随机培养基中的物体的位置（特别强调了需要长期发现检测的目标的军事应用），以及e）随机磁场（在海洋学，环境研究和医学成像等环境中产生）。该策略包括将大偏差分析与有效仿真估计器的算法设计联系起来。我们在算法的设计和性能分析中利用的关键工具是对马尔可夫链的Lyapunov界限的系统使用，并结合了重要性采样分布的参数家族。 诸如环境或自然灾害，重大市场崩溃，养老金和保险崩溃以及恐怖袭击之类的事件很少见，但结果是结果。如果成功的话，拟议的研究计划将提供有效的计算工具，以评估此类事件的风险评估，这些事件具有重型尾巴，复杂的依赖性和组合对象的合并。对稀有事实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随附的见解。示例包括计算目标能够逃避一组探测器及其有条件的位置的概率，以及评估毁灭概率，以缩小保险和金融公司的资本储备。