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

我的研究方向是研究构造多响应、多因素最优稳健设计的理论和算法，这些设计在农业、环境、工业和计算机实验中有着广泛的应用。最优稳健设计对模型的小偏差具有很强的稳健性，在实际应用中是非常有用的。随着实验成本的上升，对设计良好、节省成本的实验的需求为这一领域的继续研究提供了强大的推动力。我的研究计划包括几个研究问题，我和我的学生将在未来五年内调查这些问题。 (1)当响应变量的相关函数存在不确定性时，研究多响应模型的最优稳健设计问题。将考虑使用极小极大方法来形成稳健准则。我们将得到关于最优稳健设计的理论结果，并开发高效的数值算法来求解具有大量变量的极小极大优化问题。 (2)针对响应函数中错误规范的最优稳健设计问题将使用不同的设计准则进行研究。当实验中涉及的因素和响应变量很多时，设计问题是非常困难的。我们将发展新的设计理论和数值方法，以寻找具有多个定量和定性因素的最优稳健设计。 (3)研究多响应模型的贝叶斯设计和序贯设计问题。我们将找到有效的策略，将顺序设计用于实际应用。将进行模拟研究，以比较序贯设计和单阶段最优稳健设计。 (4)当实验中存在可能的遗漏观测时，我们将研究最优稳健设计问题。当我们构造最优设计或最优稳健设计时，我们通常假设在实际实验中没有遗漏观测。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、参与者退出医学试验等，也会发生遗漏观测的情况。在这些情况下，假设实验结束时所有观测数据都可用的最优设计可能表现不佳。因此，研究可能遗漏观测值的稳健设计问题具有重要意义。这些都是具有挑战性的问题。我们将创新方法来解决这些问题。 我相信，我的研究将极大地提高我们对所提出的问题的认识，并将为实际应用构建许多有用的设计。实验的结果将帮助我们在产品、流程、服务运营、政府政策等方面做出良好的决策。这可能会节省大量宝贵的资源，并产生显著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.