A Novel Framework for Simulation Selection Procedures Based on Multidimensional Drifting Brownian Motions Hitting Ellipsoids

本项目的研究目标是利用随机过程理论开发一种新的模拟选择程序框架。第一部分是开发基于多维漂移布朗运动撞击椭球的最佳选择的统计程序，以消除劣势系统。在这一新框架内，可以减少或完全消除因Bonferroni不平等而导致的统计程序的保守性。也要考虑对选择程序进行调整，以避免使用保守的均值假设，称为滑动配置，当竞争的备选方案数量较多时，这种假设会降低许多选择程序的效率。这项研究的第二部分使用基于多维漂移布朗运动的类似方法来开发可行性检查程序。将产生的最佳选择程序与新的可行性检查程序相结合，将允许解决受约束的最佳选择问题，其中的目标是在主要性能度量下找到最佳系统，同时还满足对次要性能度量的随机约束。这项研究引入了一种设计统计选择程序的新范式，其中必须通过实验抽样或模拟来估计其性能的系统的比较可以一次使用3个或更多系统的分组来进行，而不是使用成对比较。如果成功，这项研究有可能通过实现对劣质系统的快速筛选来显著提高这些统计选择过程的效率，这反过来又使它们适用于诸如制造、环境系统和医疗保健等大规模应用，这些应用是由于被分析系统的复杂性而使用模拟的环境的例子。

The research objective of this project is to develop a novel framework for simulation selection procedures using the theory of stochastic processes. The first part is to develop statistical procedures for selection-of-the-best which eliminate inferior systems based on multidimensional drifting Brownian motions hitting ellipsoids. Within this new framework, the conservativeness of statistical procedures due to the Bonferroni inequality can be lessened or completely eliminated. Also to be considered are adjustments in selection procedures to avoid the use of a conservative mean assumption, called slippage configuration, which deteriorates efficiency of many selection procedures when the number of competing alternatives is large. The second part of this research develops feasibility check procedures using a similar approach based on multidimensional drifting Brownian motions. Combining the resulting selection-of-the-best procedures with the new feasibility check procedures will allow solution of constrained selection-of-the-best problems, where the goal is to find the best system under a primary performance measure while also satisfying stochastic constraints on secondary performance measures. The proposed research introduces a new paradigm for designing statistical selection procedures, in which comparisons of systems whose performance must be estimated by experimental sampling or simulation, can be carried out using groups of 3 or more systems at a time rather than using pairwise comparisons. If successful, this research has the potential for dramatically increasing the efficiency of these statistical selection procedures by enabling the rapid screening of inferior systems, which in turn makes them practical for use in large-scale applications such as manufacturing, environmental systems, and health care, examples of settings where simulation is employed due to the complexity of the systems being analyzed.