Bayesian Local Kriging

Abstract : We consider the problem of constructing metamodels for computationally expensive simulation codes; that is, we construct interpolation/prediction of functions values (responses) from a finite collection of evaluations (observations). We use Gaussian process modeling and Kriging, and combine a Bayesian approach, based on a finite set of covariance functions, with the use of localized models, indexed by the point where the prediction is made. Our approach does not yield a single generative model for the unknown function, but by letting the weights of the different covariance functions depend on the prediction site, it gives enough flexibility for predictions to accommodate to non-stationarity. Contrary to Kriging prediction with plug-in parameter estimates, the resulting Bayesian predictor is constructed explicitly, without requiring any numerical optimization. It inherits the smoothness prop-erties of the covariance functions that are used and its superiority over the plug-in Kriging predictor (sometimes also called empirical-best-linear-unbiased predictor) is illustrated on various examples, including the reconstruction of an oceanographic field from a small number of observations.
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Luc Pronzato, Joaõ Rendas. Bayesian Local Kriging. Technometrics, Taylor & Francis, 2017, 59 (3), pp.293-304. ⟨http://www.tandfonline.com/doi/full/10.1080/00401706.2016.1214179⟩. ⟨hal-01093466⟩

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