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Emulation of Multivariate Simulators Using Thin-Plate Splines with Application to Atmospheric Dispersion

Emulation of Multivariate Simulators Using Thin-Plate Splines with Application to Atmospheric Dispersion
Emulation of Multivariate Simulators Using Thin-Plate Splines with Application to Atmospheric Dispersion
It is often desirable to build a statistical emulator of a complex computer simulator in order to perform analysis which would otherwise be computationally infeasible. We propose methodology to model multivariate output from a computer simulator taking into account output structure in the responses. The utility of this approach is demonstrated by applying it to a chemical and biological hazard prediction model. Predicting the hazard area which results from an accidental or deliberate chemical or biological release is imperative in civil and military planning and also in emergency response. The hazard area resulting from such a release is highly structured in space and we therefore propose the use of a thin-plate spline to capture the spatial structure and fit a Gaussian process emulator to the coefficients of the resultant basis functions. We compare and contrast four different techniques for emulating multivariate output: dimension-reduction using (i) a fully Bayesian approach with a principal component basis, (ii) a fully Bayesian approach with a thin-plate spline basis, assuming that the basis coefficients are independent, and (iii) a “plug-in” Bayesian approach with a thin-plate spline basis and a separable covariance structure; and (iv) a functional data modeling approach using a tensor-product (separable) Gaussian process. We develop methodology for the two thin-plate spline emulators and demonstrate that these emulators significantly outperform the principal component emulator. Further, the separable thin-plate spline emulator, which accounts for the dependence between basis coefficients, provides substantially more realistic quantification of uncertainty, and is also computationally more tractable, allowing fast emulation. For high resolution output data, it also offers substantial predictive and computational ad- vantages over the tensor-product Gaussian process emulator.
1323-1344
Bowman, Veronica
970ea71c-b12e-4743-b9b3-ec1dbe8401f6
Woods, David
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Bowman, Veronica
970ea71c-b12e-4743-b9b3-ec1dbe8401f6
Woods, David
ae21f7e2-29d9-4f55-98a2-639c5e44c79c

Bowman, Veronica and Woods, David (2016) Emulation of Multivariate Simulators Using Thin-Plate Splines with Application to Atmospheric Dispersion. Journal of Uncertainty Quantification, 4, 1323-1344. (In Press)

Record type: Article

Abstract

It is often desirable to build a statistical emulator of a complex computer simulator in order to perform analysis which would otherwise be computationally infeasible. We propose methodology to model multivariate output from a computer simulator taking into account output structure in the responses. The utility of this approach is demonstrated by applying it to a chemical and biological hazard prediction model. Predicting the hazard area which results from an accidental or deliberate chemical or biological release is imperative in civil and military planning and also in emergency response. The hazard area resulting from such a release is highly structured in space and we therefore propose the use of a thin-plate spline to capture the spatial structure and fit a Gaussian process emulator to the coefficients of the resultant basis functions. We compare and contrast four different techniques for emulating multivariate output: dimension-reduction using (i) a fully Bayesian approach with a principal component basis, (ii) a fully Bayesian approach with a thin-plate spline basis, assuming that the basis coefficients are independent, and (iii) a “plug-in” Bayesian approach with a thin-plate spline basis and a separable covariance structure; and (iv) a functional data modeling approach using a tensor-product (separable) Gaussian process. We develop methodology for the two thin-plate spline emulators and demonstrate that these emulators significantly outperform the principal component emulator. Further, the separable thin-plate spline emulator, which accounts for the dependence between basis coefficients, provides substantially more realistic quantification of uncertainty, and is also computationally more tractable, allowing fast emulation. For high resolution output data, it also offers substantial predictive and computational ad- vantages over the tensor-product Gaussian process emulator.

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Accepted/In Press date: 23 August 2016
Organisations: Statistics, Statistical Sciences Research Institute

Identifiers

Local EPrints ID: 347333
URI: http://eprints.soton.ac.uk/id/eprint/347333
PURE UUID: 419392eb-b56a-4f2a-b886-d3d2fef2201a
ORCID for David Woods: ORCID iD orcid.org/0000-0001-7648-429X

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Date deposited: 07 Feb 2013 12:49
Last modified: 19 Jun 2019 00:37

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Author: Veronica Bowman
Author: David Woods ORCID iD

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