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December 2011 Efficient emulators of computer experiments using compactly supported correlation functions, with an application to cosmology
Cari G. Kaufman, Derek Bingham, Salman Habib, Katrin Heitmann, Joshua A. Frieman
Ann. Appl. Stat. 5(4): 2470-2492 (December 2011). DOI: 10.1214/11-AOAS489

Abstract

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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Cari G. Kaufman. Derek Bingham. Salman Habib. Katrin Heitmann. Joshua A. Frieman. "Efficient emulators of computer experiments using compactly supported correlation functions, with an application to cosmology." Ann. Appl. Stat. 5 (4) 2470 - 2492, December 2011. https://doi.org/10.1214/11-AOAS489

Information

Published: December 2011
First available in Project Euclid: 20 December 2011

zbMATH: 1234.62166
MathSciNet: MR2907123
Digital Object Identifier: 10.1214/11-AOAS489

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.5 • No. 4 • December 2011
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