Workshop on New Directions in Monte Carlo Methods

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很长时间了，但它们所应用的问题已经发生了巨大的变化。蒙特卡罗方法现在被常规地应用于非常复杂的问题，例如具有大量预测器的贝叶斯回归模型和涉及多个水平的贝叶斯分层模型。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已经朝着几个新的方向进行。例如，由于在高度复杂的模型中，不再可能分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，自动演变为对当前问题最优的算法。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，先验被放置在潜在模型的集合上，研究人员希望获得模型的后验分布以及模型的参数。因为不同模型的参数可能有不同的维度，所以用于估计后验分布的马尔科夫链必须是“跨维的”。在这个研讨会上，十二位在蒙特卡洛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。蒙特卡洛模拟是一种方法，它使用随机抽样来得出无法准确计算的量的数值近似。这种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如此复杂，以至于不可能获得准确的解，如果一个人愿意使用蒙特卡罗模拟提供的近似解，那么仍然可以考虑该模型。计算能力的最新进展使蒙特卡罗模拟变得越来越准确和有用，但仍有许多问题有待解决。讲习班为该领域的老牌研究人员以及新来者提供了一个极好的机会，以讨论过去十年取得的重大进展；讨论哪些有效，哪些无效；并确定重要问题和新的研究方向。

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.