Efficient emulators of computer experiments using compactly supported correlation functions, with an application to cosmology

Details Efficient emulators of computer experiments using compactly supported correlation functions, with an application to cosmology Efficient emulators of computer experiments using compactly supported correlation functions, with an application to cosmology

2011-07-04

arxiv.org/abs/1107.0749v2

Annals of Applied Statistics 2011, Vol. 5, No. 4, 2470-2492

Statistics

Methodology

Published in at http://dx.doi.org/10.1214/11-AOAS489 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

10.1214/11-AOAS489

Statistical emulators of computer simulators have proven to be useful in a variety of applications. The widely adopted model for emulator building, using a Gaussian process model with strictly positive correlation function, is computationally intractable when the number of simulator evaluations is large. We propose a new model that uses a combination of low-order regression terms and compactly supported correlation functions to recreate the desired predictive behavior of the emulator at a fraction of the computational cost. Following the usual approach of taking the correlation to be a product of correlations in each input dimension, we show how to impose restrictions on the ranges of the correlations, giving sparsity, while also allowing the ranges to trade off against one another, thereby giving good predictive performance. We illustrate the method using data from a computer simulator of photometric redshift with 20,000 simulator evaluations and 80,000 predictions.

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