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

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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.