Combining EM and Monte Carlo to Maximize Intractable Likelihood Functions

结合 EM 和蒙特卡罗来最大化棘手的似然函数

• 批准号: 0072827
• 负责人: James Hobert
• 金额: $ 34.59万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-15 至 2004-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072827&HistoricalAwards=false
• 关键词: Combining; EM; Monte; Carlo; Maximize

ABSTRACTThis proposal concerns parameter estimation methodology for animportant class of statistical models. These models, which we referto as ``generalized hierarchical models'' (GHMs), have proven to beextremely useful in a wide range of scientific endeavors. Specificexamples of applications that have appeared in the scientificliterature include: the impact of passive smoking, changes in votingbehavior, clinical trials for a treatment for epilepsy, social surveysof households in rural China, sheep cloning experiments, theestimation of animal abundance and the analysis of multivariatesurvival data.A general purpose algorithm for estimation called EM(expectation-maximization) is particularly suited to the GHM setting.However, implementation the algorithm is complicated because it ofteninvolves the calculation of intractable multi-dimensional integrals.Two methods for dealing with these integrals that have received someattention recently are Monte Carlo EM (MCEM) and StochasticApproximation EM (SAEM). Both methods involve replacing intractableintegrals by Monte Carlo approximations. Unfortunately, applicationsof the these Monte Carlo fitting algorithms to GHMs can often takehours or even days to converge. This has limited their widespread useso far. The situation will no doubt improve with the availability offaster computers. However, the development of much faster algorithmswould accelerate this process tremendously. Hence, the proposedresearch concerns a detailed comparison of the MCEM and SAEMalgorithms with a view towards substantially improving theirperformance.

摘要本建议涉及一类重要的统计模型的参数估计方法。 这些模型，我们称之为“广义层次模型”（GHM），已被证明在广泛的科学工作中非常有用。 科学文献中出现的具体应用实例包括：被动吸烟的影响，投票行为的变化，癫痫治疗的临床试验，中国农村家庭的社会调查，绵羊克隆实验，动物丰度的估计和多变量生存数据的分析。（期望最大化）特别适合于GHM设置。然而，实现该算法是复杂的，因为它经常涉及到计算棘手的多维积分。两种方法来处理这些积分，最近得到了一些关注，随机近似EM（StochasticApproximation EM，SAEM）。 这两种方法都涉及用蒙特卡罗近似代替难以解决的积分。 不幸的是，这些蒙特卡罗拟合算法的GHM的applications往往需要几个小时甚至几天的收敛。 这就限制了它们的广泛使用。 随着更先进的计算机的出现，情况无疑会有所改善。 然而，更快的算法的发展将大大加速这一过程。 因此，拟议的研究关注的MCEM和SAEM算法的详细比较，以期大大提高其性能。