Combining EM and Monte Carlo to Maximize Intractable Likelihood Functions

本建议涉及一类重要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极其有用。科学文献中出现的具体应用例子包括：被动吸烟的影响，投票行为的改变，治疗癫痫的临床试验，农村中国家庭的社会调查，绵羊克隆实验，动物数量的估计和多变量生存数据的分析。一种称为EM(期望最大化)的通用估计算法特别适合于GHM设置。但是，该算法的实现很复杂，因为它经常涉及到难以处理的多维积分的计算。最近受到关注的两种处理这些积分的方法是蒙特卡罗EM和随机逼近EM。这两种方法都涉及用蒙特卡罗近似代替难以处理的积分。不幸的是，这些蒙特卡罗拟合算法在温室气体中的应用往往需要几个小时甚至几天的时间才能收敛。这限制了它们到目前为止的广泛使用。随着更大型计算机的问世，情况无疑会有所改善。然而，更快的算法的开发将极大地加速这一过程。因此，本研究对MCEM和SAEM算法进行了详细的比较，以期显著提高它们的性能。

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.