This proposal concerns parameter estimation methodology for an important class of statistical models. These models, which we refer to as ``generalized hierarchical models'' (GHMs), have proven to be extremely useful in a wide range of scientific endeavors. Specific examples of applications that have appeared in the scientific literature include: the impact of passive smoking, changes in voting behavior, clinical trials for a treatment for epilepsy, social surveys of households in rural China, sheep cloning experiments, the estimation of animal abundance and the analysis of multivariate survival 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 often involves the calculation of intractable multi-dimensional integrals. Two methods for dealing with these integrals that have received some attention recently are Monte Carlo EM (MCEM) and Stochastic Approximation EM (SAEM). Both methods involve replacing intractable integrals by Monte Carlo approximations. Unfortunately, applications of the these Monte Carlo fitting algorithms to GHMs can often take hours or even days to converge. This has limited their widespread use so far. The situation will no doubt improve with the availability of faster computers. However, the development of much faster algorithms would accelerate this process tremendously. Hence, the proposed research concerns a detailed comparison of the MCEM and SAEM algorithms with a view towards substantially improving their performance.
