Optimal experimental designs and response-adaptive designs

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Optimization serves as a basic tool in most areas of the theoretical and applied sciences. The present proposal highlights the need for objective methodologies for optimization problems in optimal designs and response-adaptive designs with potential applications.******A statistical model is affected by problems associated with efficient estimation of parameters when the data do not contain enough information. This problem arises in latent variable models. We need to determine optimal designs to maximize the information with a small sample size. I first plan to work on maximum likelihood estimation of the parameters of latent variable models for paired comparisons. I then extend the work to general class of such models that apply to other fields of research, such as sports and machine learning.******In optimal design, we generally assume that the model is known at the design stage. However, in many situations this is not the case. We need to implement a design that is efficient for two or more models, to discriminate, and to select the best model. I plan to work on a constrained optimization approach for model discrimination, and then study aspects of adaptive sequential design that will simultaneously achieve the objectives of selecting the correct model and estimating the parameters efficiently. I also plan to work on optimization problems with respect to several distributions, and apply the methods to areas such as image processing. A common problem is to have incomplete information on true states of the pixels of a picture or a graph. I plan to develop optimal design methods that will provide ways of decreasing ambiguity and increasing consistency of an initial stochastic labeling.******Response-adaptive designs are becoming increasingly popular nowadays. Several response-adaptive designs have been developed, however, there has been limited effort in applying these to circular data. Motivated by this, I propose to develop allocation designs for a general class of circular responses, and work on a practical data sets on comparative prospective randomized interventional trials. Most of such data involve various covariates which may influence the responses. Quite naturally, the next step is to induce these covariates in the model, so as to achieve more efficient designs.******The proposed research will provide opportunities for training of highly qualified personnel at all levels. They will learn statistical theories in the areas of latent variable models (with applications in sports and machine learning) and model discrimination (with applications in industrial and chemical engineering for carrying out tests for models). The response-adaptive designs for circular data will provide practical tools to applied researchers in biomedical studies, meteorology and astronomy as circular data arise naturally in these scientific studies.