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

要研究的问题主要有四个方面：试验和优化设计的贝叶斯比较、稳健贝叶斯研究中的分层模型、随机优化和文件合并方法的统计方面。将开发文件合并方法的统计理论，这种方法在评估联邦机构的政策影响时被大量使用。为了为多阶段概率模型的应用提供坚实的理论基础，我们将研究稳健贝叶斯分析的层次模型领域。随机优化项目的目标是开发一种基本上自动化的、可能快速收敛的算法，用于寻找复杂函数的全局最小值。在贝叶斯比较实验区，将研究新的工具和理论，以选择两个实验中较好的一个。最优试验设计理论将被应用于一些模型，这些模型存在流行的设计，但对它们的最优性知之甚少。还将在各种假设下对量子响应的自适应贝叶斯设计进行研究，这将对生物统计学应用非常有用。如果在临床试验中采用，它们应该会节省时间。运用优化设计理论对稳健设计、工艺设计和计算机实验设计中存在的问题进行分析。

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.