Mathematical Sciences: Bayesian Design and Analysis, Stochastic Optimization, and File-Merging Methodology

点击翻译按钮获取中文摘要

The research problems to be studied belong mainly to four areas: Bayesian comparison of experiments and optimal designs, hierarchical models in robust Bayes studies, stochastic optimization, and statistical aspects of file-merging methodology. The statistical theory for file-merging methodology, which is used heavily in evaluating policy implications by federal agencies, will be developed. To provide a solid theoretical foundation for usage of multi-stage probability models the area of hierarchical models for robust Bayes analysis will be studied. The goal of a stochastic optimization project is the development of a mostly automated and possibly fast converging algorithm for finding the global minimum of a complicated function. In the Bayesian comparison of experiments area, new tools and theories will be investigated for choosing the better of two experiments. Optimal experimental design theory will be applied to a number of models for which popular designs exist but little is known concerning their optimality properties. Research will also be conducted on adaptive Bayesian designs for quantal response under a variety of assumptions which will be very useful for biostatistical applications. If adopted in clinical trials, they should lead to time savings. Problems in robust design, process design and design of computer experiments will be analyzed through the application of optimal design theory.