Computer Experiments and Multi-stage Factorial Designs

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My research program will focus on the design and analysis of (a) computer experiments and (b) multi-stage factorial experiments with randomization restrictions. Computer simulators are often used to model extremely expensive or unobservable complex physical systems. Realistic simulators of complex processes can still be expensive to run, and a statistical surrogate is used for experimentation. Important current research topics include surrogate modeling, design of experiments, integrating various sources of data, inverse problem and uncertainty quantification (an emerging area). Dynamic computer simulators is an active research area, and scientists are interested in efficient designs for estimating process features (e.g., global minimum, contour). I am proposing innovative ideas for generalizing my contour estimation method (for scalar valued simulators) to solve the inverse problem when the simulator returns a time series output. As part of this research program, I will invent new surrogates for simulators that cannot be emulated by conventional Gaussian process models. For instance, I am developing a new hierarchical Gamma process model with Gaussian latent variables for emulating simulators with positive responses. The existence and construction of designs for multi-stage factorial experiments with randomization restrictions (e.g., split-lot designs) is a challenging problem. I proposed a finite projective geometry (PG) approach which establishes the existence results and facilitates easy construction of such designs via spread (partition into subspaces) and stars (subspaces with common overlap) of PG. My proposed research will focus of finding optimal fractional factorial designs under this unified framework. More interestingly, I have discovered a new class of Latin hypercube designs (LHDs) that can be constructed from stars. These designs have geometric properties that are useful for generating space-filling LHDs, a very popular design in computer experiments.