  In computer experiments, a mathematical model implemented on a computer is
used to represent complex physical phenomena. These models, known as computer
simulators, enable experimental study of a virtual representation of the
complex phenomena. Simulators can be thought of as complex functions that take
many inputs and provide an output. Often these simulators are themselves
expensive to compute, and may be approximated by "surrogate models" such as
statistical regression models. In this paper we consider a new kind of
surrogate model, a Bayesian ensemble of trees (Chipman et al. 2010), with the
specific goal of learning enough about the simulator that a particular feature
of the simulator can be estimated. We focus on identifying the simulator's
global minimum. Utilizing the Bayesian version of the Expected Improvement
criterion (Jones et al. 1998), we show that this ensemble is particularly
effective when the simulator is ill-behaved, exhibiting nonstationarity or
abrupt changes in the response. A number of illustrations of the approach are
given, including a tidal power application.
