Adaptive Markov Chain Monte Carlo methods

自适应马尔可夫链蒙特卡罗方法

• 批准号: 0906631
• 负责人: Yves Atchade
• 金额: $ 9.96万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 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: 2009-08-01 至 2012-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0906631&HistoricalAwards=false
• 关键词: Adaptive; Markov; Chain; Monte; Carlo

This award is funded under the American Recovery and Reinvestment Act of2009 (Public Law 111-5).Markov Chain Monte Carlo (MCMC) is a flexible computational technique thathas proven very useful to many scientific disciplines and is the backboneof current implementations of Bayesian inference. Recent researchdevelopments suggest that the use of adaptive methods can make Monte Carloalgorithms considerably more effective. This research proposal has twomajor components. The first part will contribute to the development of alimit theory for adaptive MCMC algorithms. More Specifically, the PI willdevelop a resolvent-based martingale approximation technique to investigatethe central limit theorem and the asymptotic variance estimation forvarious adaptive MCMC algorithms. The second part of this research activitywill develop a new MCMC algorithm for the Bayesian analysis of statisticalmodels with intractable normalizing constants, a topic that currently posesmajor computational challenges. This part of the research is driven by theprotein design problem in computational biology but the same problem alsofrequently occurs in many other statistical models including Markov randomfields, Markov point processes.Markov Chain Monte Carlo is a well-established Monte Carlo technique forsampling probability distributions. The method is used widely to solvesubstantive problems in many areas of applications. It is especially usefulin situations with high-dimensional data, which is increasingly common inscience and engineering research as well as applications. Thus, theresearch developments from this project can have a significant impact onmethods for doing statistical inference in these areas. Through itstheoretical component, this research project will advance the generalunderstanding and strengthen the use of adaptive Monte Carlo methods inpractice. In the course of developing the asymptotic theory, the PI willdevelop original extensions to some well-established probabilistic tools.The research is also proposing a new algorithm to tackle one of the mostchallenging current problem in Monte Carlo simulation; sampling from theposterior distribution of statistical models with intractable normalizingconstants.

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。马尔可夫链蒙特卡罗（MCMC）是一种灵活的计算技术，已被证明对许多科学学科非常有用，是当前贝叶斯推理实现的支柱。最近的研究进展表明，使用自适应方法可以使蒙特卡罗算法相当有效。这个研究计划有两个主要组成部分。第一部分将有助于自适应MCMC算法的极限理论的发展。更具体地说，PI将开发一种基于解析的鞅近似技术，以研究各种自适应MCMC算法的中心极限定理和渐近方差估计。本研究活动的第二部分将开发一种新的MCMC算法，用于统计模型的贝叶斯分析，该模型具有难以处理的归一化常数，这是目前具有主要计算挑战的主题。这部分研究是由计算生物学中的蛋白质设计问题驱动的，但同样的问题也经常发生在许多其他统计模型中，包括马尔可夫随机场，马尔可夫点过程。马尔可夫链蒙特卡罗是一种成熟的蒙特卡罗抽样概率分布技术。该方法被广泛用于解决许多应用领域的实质性问题。它在高维数据的情况下特别有用，这在科学和工程研究以及应用中越来越普遍。因此，该项目的研究进展可以对这些领域的统计推断方法产生重大影响。通过其理论组成部分，本研究项目将促进对自适应蒙特卡罗方法的一般理解，并加强其在实践中的应用。在发展渐近理论的过程中，PI将对一些已建立的概率工具进行原始扩展。该研究还提出了一种新的算法来解决蒙特卡罗模拟中当前最具挑战性的问题之一；从具有难以处理的归一化常数的统计模型的后验分布中抽样。