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Sequential design for computer experiments with a flexible Bayesian additive model. (English. French summary) Zbl 1349.62366

Summary: 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 [the first author et al., Ann. Appl. Stat. 4, No. 1, 266–298 (2010; Zbl 1189.62066)], 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 [D. R. Jones et al., J. Glob. Optim. 13, No. 4, 455–492 (1998; Zbl 0917.90270)], 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.

MSC:

62L05 Sequential statistical design
62G08 Nonparametric regression and quantile regression
62P12 Applications of statistics to environmental and related topics

Software:

EGO; BayesTree; lhs; BartPy
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Full Text: DOI arXiv

References:

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