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Bayesian Local Kriging

Summary: We consider the problem of constructing metamodels for computationally expensive simulation codes; that is, we construct interpolators/predictors of functions values (responses) from a finite collection of evaluations (observations). We use Gaussian process (GP) modeling and kriging, and combine a Bayesian approach, based on a finite set GP models, with the use of localized covariances indexed by the point where the prediction is made. Our approach is not based on postulating a generative model for the unknown function, but by letting the covariance functions depend on the prediction site, it provides enough flexibility to accommodate arbitrary nonstationary observations.

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  • Topics: Statistics
  • Keywords: Bayesian kriging, Computer experiments, Interpolation, Nonstationary process, Prediction, Random field
  • Author: Pronzato, Luc; Rendas, Maria-João
  • Journal: Technometrics