多响应计算机试验的设计与分析

Design and analysis of experiments is one of the oldest and most applicable branches in statistics. It has many applications in industrial and agricultural production and science. With the development of science and technology, a number of experiments with high cost can be replaced or partially replaced by computer simulations. Consequently, design and analysis of computer experiments, as an emerging area in design and analysis of experiments, has appeared. This project will study design and analysis of multi-response computer experiments, which include multi-fidelity computer experiments, vector-response computer experiments, and computer experiments with qualitative factors. We will focus on (1) reasonable nested and sliced criteria under multi-response Gaussian process models, and construction of optimal or nearly optimal designs with respect to these criteria by new optimization techniques; (2) solutions to statistical inferential issues in multi-response Gaussian process models with the generalized inference, including hypothesis testing and interval estimation, and frequentist properties of the solutions.

“试验的设计与分析”这一学科是统计学中发展最早、应用最广的分支之一，在工、农业生产等领域应用很广。随着科技的发展，很多成本较高的试验可以通过计算机仿真计算代替或部分代替。由此在试验设计中产生了一个新兴领域：计算机试验的设计与分析。本项目研究多响应计算机实验的设计与分析。这里的多响应试验包括多精度计算机试验、向量值响应计算机试验以及含有定性因子的计算机试验。重点研究(1)在多响应高斯过程模型下合理的嵌套、分片试验设计准则，结合优化领域研究中的最新成果给出在这些准则下的最优或近似最优设计；(2)将广义推断等统计推断方法用于多响应高斯过程模型中的推断问题，包括构造假设检验、区间估计等，并讨论它们的频率性质。

本项目研究了多精度计算机试验，向量值响应计算机试验和含有定性因子的计算机试验。重点研究了在多响应高斯过程模型下合理的嵌套、分片试验设计准则，并结合一些优化领域研究中的最新成果给出了在这些准则下的最优或近似最优设计；同时，将广义推断等统计推断方法用在了多响应高斯过程模型中的推断问题中，给出了假设检验、区间估计并讨论了它们的频率性质。