Bayesian treed gaussian process models

Computer experiments often require dense sweeps over input parameters to obtain a qualitative understanding of their response. Such sweeps can be prohibitively expensive, and are unnecessary in regions where the response is easily predicted; well-chosen designs could allow a mapping of the response with far fewer simulation runs. Thus, there is a need for computationally inexpensive surrogate models and an accompanying method for selecting small designs. This dissertation explores a nonparametric and semiparametric nonstationary modeling methodologies for addressing this need that couples stationary Gaussian processes and (limiting) linear models with treed partitioning. A Bayesian perspective yields an explicit measure of (nonstationary) predictive uncertainty that can be used to guide sampling. As typical experiments are high-dimensional and require large designs, a careful but thrifty implementation is essential. The methodological developments and statistical computing details which make this approach efficient are outlined in detail. In addition to several illustrations using synthetic data, classic nonstationary data analyzed in recent literature are used to validate the model, and the benefit of adaptive sampling is illustrated through a motivating example which involves the computational fluid dynamics simulation of a NASA reentry vehicle.