Combining EM and Monte Carlo to Maximize Intractable Likelihood Functions

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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.