Workshop on New Directions in Monte Carlo Methods

蒙特卡罗方法新方向研讨会

• 批准号: 1241502
• 负责人: Hani Doss
• 金额: $ 0.86万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1241502&HistoricalAwards=false
• 关键词: Workshop; New; Directions; Monte; Carlo

The workshop will be held January 18-19, 2013, on the campus of the University of Florida. Although Monte Carlo methods have existed for a long time, the problems to which they are applied have changed dramatically. Monte Carlo methods are now routinely applied to very complex problems, for instance Bayesian regression models with a large number of predictors and Bayesian hierarchical models involving many levels. To address this increased complexity, recent research on Monte Carlo approaches has proceeded in several new directions. For example, because in highly complex models it is no longer possible to analytically devise Monte Carlo algorithms which are optimal or near-optimal, researchers have developed "adaptive MCMC algorithms" which, as they are running, automatically evolve into algorithms which are optimal for the current problem. Another example involves Bayesian model selection, where researchers have many models that can be used to explain the data, and they wish to select the best one. In a Bayesian approach, a prior is placed on the set of potential models, and the researcher wishes to obtain the posterior distribution of the models, and the parameters for the models. Because the parameters for the different models may have different dimensions, Markov chains for estimating posterior distributions must be "transdimensional." In this workshop, twelve distinguished individuals who work in Monte Carlo simulation review the current state of the field and present their recent work. A number of young researchers will also participate in the workshop and present their work in poster sessions.Monte Carlo simulation is a methodology that uses random sampling to arrive at numerical approximations to quantities that cannot be computed exactly. The methodology allows researchers to use extremely complex statistical models: if a potentially useful model is so complicated that it is not possible to obtain exact solutions, the model can still be considered if one is willing to use approximate solutions provided by Monte Carlo simulation. Recent advances in computing power have made Monte Carlo simulation increasingly accurate and useful, but many unsolved problems remain. The workshop provides an excellent opportunity for established researchers in the field, as well as newcomers, to discuss the significant developments that have taken place in the last decade; to discuss what works and what does not; and to identify important problems and new research directions.

研讨会将于2013年1月18日至19日在佛罗里达大学校园举行。虽然蒙特卡罗方法已经存在了很长时间，但应用它的问题已经发生了巨大的变化。蒙特卡罗方法现在经常应用于非常复杂的问题，例如具有大量预测因子的贝叶斯回归模型和涉及许多层次的贝叶斯分层模型。为了解决这种日益增加的复杂性，最近对蒙特卡罗方法的研究在几个新的方向上进行。例如，因为在高度复杂的模型中，不再可能解析地设计出最优或接近最优的蒙特卡罗算法，研究人员开发了“自适应MCMC算法”，当它们运行时，会自动进化成当前问题的最优算法。另一个例子涉及贝叶斯模型选择，研究人员有许多模型可以用来解释数据，他们希望选择最好的一个。在贝叶斯方法中，对潜在模型集进行先验处理，研究者希望获得模型的后验分布和模型的参数。因为不同模型的参数可能有不同的维度，估计后验分布的马尔可夫链必须是“跨维度的”。在本次研讨会中，十二位在蒙特卡罗模拟领域工作的杰出人士回顾了该领域的现状并介绍了他们最近的工作。一些年轻的研究人员也将参加研讨会，并在海报会议上展示他们的工作。蒙特卡罗模拟是一种方法，它使用随机抽样来达到不能精确计算的数量的数值近似。该方法允许研究人员使用极其复杂的统计模型：如果一个潜在有用的模型非常复杂，以至于不可能获得精确解，如果愿意使用蒙特卡罗模拟提供的近似解，仍然可以考虑该模型。最近计算能力的进步使蒙特卡罗模拟越来越准确和有用，但仍有许多未解决的问题。研讨会为该领域的知名研究人员以及新来者提供了一个极好的机会，讨论过去十年中发生的重大发展；讨论什么可行，什么不可行；并找出重要的问题和新的研究方向。