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In computer experiments, a mathematical model implemented on a computer isused to represent complex physical phenomena. These models, known as computersimulators, enable experimental study of a virtual representation of thecomplex phenomena. Simulators can be thought of as complex functions that takemany inputs and provide an output. Often these simulators are themselvesexpensive to compute, and may be approximated by "surrogate models" such asstatistical regression models. In this paper we consider a new kind ofsurrogate model, a Bayesian ensemble of trees (Chipman et al. 2010), with thespecific goal of learning enough about the simulator that a particular featureof the simulator can be estimated. We focus on identifying the simulator'sglobal minimum. Utilizing the Bayesian version of the Expected Improvementcriterion (Jones et al. 1998), we show that this ensemble is particularlyeffective when the simulator is ill-behaved, exhibiting nonstationarity orabrupt changes in the response. A number of illustrations of the approach aregiven, including a tidal power application.

Sequential Design for Computer Experiments with a Flexible Bayesian Additive Model