Sequential Design for Computer Experiments with a Flexible Bayesian Additive Model

Details Sequential Design for Computer Experiments with a Flexible Bayesian Additive Model Sequential Design for Computer Experiments with a Flexible Bayesian Additive Model

2012-03-06

arxiv.org/abs/1203.1078v1

Statistics

Methodology

19 pages

Scientific paper

In computer experiments, a mathematical model implemented on a computer, is used to represent complex physical phenomena. These models, known as 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, 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 a modification 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 discontinuities in the response. A number of illustrations of the approach are given, including a tidal power application.

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