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The effect of the nugget on Gaussian process emulators of computer models

The effect of the nugget on Gaussian process emulators of computer models
The effect of the nugget on Gaussian process emulators of computer models
The effect of a Gaussian process parameter known as the nugget, on the development of computer model emulators is investigated. The presence of the nugget results in an emulator that does not interpolate the data and attaches a non-zero uncertainty bound around them. The limits of this approximation are investigated theoretically, and it is shown that they can be as large as those of a least squares model with the same regression functions as the emulator, regardless of the nugget’s value. The likelihood of the correlation function parameters is also studied and two mode types are identified. Type I modes are characterised by an approximation error that is a function of the nugget and can therefore become arbitrarily small, effectively yielding an interpolating emulator. Type II modes result in emulators with a constant approximation error. Apart from a theoretical investigation of the limits of the approximation error, a practical method for automatically imposing restrictions on its extent is introduced. This is achieved by means of a penalty term that is added to the likelihood function, and controls the amount of unexplainable variability in the computer model. The main findings are illustrated on data from an Energy Balance climate model.
Computer experiments, Ill conditioning, Interpolation, Approximation, Kriging
0167-9473
4215-4228
Andrianakis, Ioannis
130365dc-7914-4b33-87b2-92eca9da10a5
Challenor, Peter G.
a7e71e56-8391-442c-b140-6e4b90c33547
Andrianakis, Ioannis
130365dc-7914-4b33-87b2-92eca9da10a5
Challenor, Peter G.
a7e71e56-8391-442c-b140-6e4b90c33547

Andrianakis, Ioannis and Challenor, Peter G. (2012) The effect of the nugget on Gaussian process emulators of computer models. Computational Statistics & Data Analysis, 56 (12), 4215-4228. (doi:10.1016/j.csda.2012.04.020).

Record type: Article

Abstract

The effect of a Gaussian process parameter known as the nugget, on the development of computer model emulators is investigated. The presence of the nugget results in an emulator that does not interpolate the data and attaches a non-zero uncertainty bound around them. The limits of this approximation are investigated theoretically, and it is shown that they can be as large as those of a least squares model with the same regression functions as the emulator, regardless of the nugget’s value. The likelihood of the correlation function parameters is also studied and two mode types are identified. Type I modes are characterised by an approximation error that is a function of the nugget and can therefore become arbitrarily small, effectively yielding an interpolating emulator. Type II modes result in emulators with a constant approximation error. Apart from a theoretical investigation of the limits of the approximation error, a practical method for automatically imposing restrictions on its extent is introduced. This is achieved by means of a penalty term that is added to the likelihood function, and controls the amount of unexplainable variability in the computer model. The main findings are illustrated on data from an Energy Balance climate model.

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Published date: 2012
Keywords: Computer experiments, Ill conditioning, Interpolation, Approximation, Kriging
Organisations: Marine Systems Modelling

Identifiers

Local EPrints ID: 343348
URI: https://eprints.soton.ac.uk/id/eprint/343348
ISSN: 0167-9473
PURE UUID: b2874514-9df8-42a2-82f4-8479ac7cdeb4

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Date deposited: 01 Oct 2012 15:49
Last modified: 16 Jul 2019 21:53

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