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  1. Single nugget Kriging

    Lee, Minyong R.
    Stanford, Calif. : Department of Statistics, Stanford University, November 2015.

    Online statistics.stanford.edu

  2. Prediction and dimension reduction methods in computer experiments [electronic resource]

    Lee, Minyong R.
    2017.

    In many fields of engineering and science, computer experiments have become essential tools in studying physical processes. This dissertation reviews standard prediction methods and dimension reduction methods in the analysis of computer experiments and proposes new approaches. Response surface modeling is the starting point of the analysis of computer experiments. Kriging or Gaussian process regression is widely used in constructing response surfaces. We propose Single Nugget Kriging, which is a method with better predictions at extreme values than the standard method of Kriging. Our prediction exhibits robustness to the model mismatch in the covariance parameters, a desirable feature for computer simulations with a restricted number of data points. For high dimensional computer experiments, dimension reduction methods in regression are essential for solving optimization problems and inverse problems. We compare model-free sufficient dimension reduction methods and the active subspace for computer experiments. We propose a modification of the active subspace. We further discuss the analysis of dimension reduction methods in computer experiments, using projected Gaussian processes.

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