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.

摘要此提案涉及动画类统计模型类别的参数估计方法。 这些模型被称为``广义层次模型''（GHM），已被证明在广泛的科学努力中很有用。 科学文学中出现的应用的指定样本包括：被动吸烟的影响，投票行为的变化，癫痫病治疗的临床试验，中国农村的家庭监测，绵羊克隆实验的社会监测，尤其是估算的估计，估计多个Algorimimiation Algorith Algorith Algorith Algorith Amaximization Aquorith aquorith aquorith aquorith a imimizima and-Maximization Aquorith aquorith aquorith aquorith am Maximization am Maximization aquorith aquorith aquorith aquorith aquorith am-aporiation（适用于GHM设置。但是，实施算法很复杂，因为它经常引起棘手的多维积分的计算。这是处理最近收到的这些积分的两种方法是蒙特卡洛EM（MCEM）EM（McEm）和StochasticApproximation Em（Saem）。 两种方法都涉及用蒙特卡洛近似替换顽固的整合性。 不幸的是，这些蒙特卡洛拟合算法对GHM的应用通常需要花费小时甚至几天才能收敛。 这限制了他们的广泛使用。 毫无疑问，这种情况将随着供应量的卸载计算机而改善。 但是，更快的算法的发展大大加速了这一过程。 因此，提议的研究涉及MCEM和Saemalgorithms的详细比较，以实质上改善其性能。