Optimal robust design and estimation for multi-response, multi-factor and multi-view models

我的研究项目侧重于研究多响应和多因素实验的最优稳健设计的理论和算法，在农业，环境，工业和计算机实验中有广泛的应用。最优鲁棒设计对小模型偏差具有鲁棒性，在实际应用中具有重要意义。随着实验成本的上升，对设计良好的实验以节省成本的需求为这一领域的持续研究提供了强大的动力。 我的研究计划包括几个研究问题，我的学生和我将在未来五年内调查。 (1)研究了响应变量的相关函数中存在不确定性时多响应模型的最优鲁棒设计问题。 将考虑采用极大极小法来形成稳健性标准。 我们将推导出最优稳健设计的理论结果，并开发出求解具有大量变量的极大极小优化问题的有效数值算法。 (2)针对响应函数中的误设定的最优鲁棒设计问题将使用各种设计准则进行研究。 当试验涉及的因素和响应变量较多时，设计问题是一个非常难解决的问题。我们将开发新的设计理论和数值方法，以找到具有多个定量和定性因素的最佳稳健设计。 (3)我们还将研究多响应模型的贝叶斯和序贯设计问题。我们将找到有效的策略来使用实际应用的顺序设计。将进行模拟研究，以比较序贯设计与一阶段最优稳健设计。 (4)我们将研究最优稳健设计问题时，有可能在实验中丢失的意见。在构造最优设计或最优稳健设计时，我们通常假设在实际试验中不存在缺失观测。然而，即使在设计良好的实验中，由于各种原因，如工程实验中的仪器故障，参与者退出医学实验，也会发生观察缺失。 在这些情况下，假设所有观测在实验结束时都可用的最优设计可能会表现不佳。因此，研究具有可能缺失观测值的稳健设计问题是非常重要的。 这些都是具有挑战性的问题。我们将开发创新方法来解决这些问题。 我相信，我的研究将显着推进我们的知识提出的问题，我们将构建许多有用的设计，为实际应用。实验的结果将帮助我们在产品、工艺、服务运营、政府政策等方面做出正确的决策，从而节省大量宝贵的资源，产生重大的社会效益和经济效益。

My research program focuses on studying theories and algorithms for constructing optimal robust designs of experiments with multiple responses and multiple factors, which have a wide range of applications in agricultural, environmental, industrial, and computer experiments. Optimal robust designs, which are robust against small model departures, are very useful for practical applications. As the cost of experiments rises, the need for well-designed experiments that save costs provides a powerful impetus for the continuing research in this area. My research program includes several research problems that my students and I will investigate in the next five years. (1) Optimal robust design problems for multi-response models will be studied when there are uncertainties in the correlation functions of the response variables. A minimax approach will be considered to form the robust criterion. We will derive theoretical results about the optimal robust designs, and develop efficient numerical algorithms for solving minimax optimization problems with a large number of variables. (2) Optimal robust design problems against misspecifications in the response functions will be investigated using various design criteria. When there are many factors and response variables involved in the experiment, the design problem is extremely hard to solve. We will develop new design theory and numerical methods for finding optimal robust designs with multiple quantitative and qualitative factors. (3) We will also study Bayesian and sequential design problems for multi-response models. We will find effective strategies to use sequential designs for practical applications. Simulation studies will be conducted to compare sequential designs with one-stage optimal robust designs. (4) We will investigate optimal robust design problems when there are possible missing observations in the experiment. We usually assume that there are no missing observations in the actual experiment when we construct optimal designs or optimal robust designs. However, missing observations do happen even under well designed experiments due to various reasons, such as instrument malfunction in engineering experiments, participants dropping out of medical trials. Under these situations, optimal designs that assume all the observations are available at the end of the experiment may perform poorly. Thus, it is important to study robust design problems with possible missing observations. These are challenging problems. We will develop innovative methods to solve these problems. I believe that my research will significantly advance our knowledge of the proposed problems and we will construct many useful designs for practical applications. The results from experiments will help us make good decisions on products, processes, service operations, government policies, and so on. This may result in huge savings in valuable resources, and generate significant social and economic benefits.