Robert B. Gramacy, Herbert K. H. Lee, William MacReady
12/31/2005 09:00 AM
Applied Mathematics & Statistics
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. We explore a non-stationary modeling methodology for addressing this need that couples stationary Gaussian process with treed partitioning. A Bayesian perspective yields an explicit measure of (non-stationary) 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. Thus, the statistical computing details which make our methodology efficient are outlined in detail. Classic non-stationary data analyzed in recent literature is used to validate our model, and the benefit of adaptive sampling is illustrated through our motivating example which involves the computational fluid dynamics simulation of a NASA reentry vehicle.
