The effect of the nugget on Gaussian process emulators of computer models
The effect of the nugget on Gaussian process emulators of computer models
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DOI：
10.1016/j.csda.2012.04.020
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发表时间：
2012-12-01
影响因子：
1.8
通讯作者：
Challenor, Peter G.
中科院分区：
文献类型：
--
作者：
Andrianakis, Ioannis;Challenor, Peter G.
高斯过程参数被称为金块，对计算机模型仿真器的发展的影响进行了研究。块金的存在导致仿真器不对数据进行插值，并在其周围附加非零不确定性。理论上研究了这种近似的极限，结果表明，它们可以像仿真器具有相同回归函数的最小二乘模型一样大，而不管块金的值如何。还研究了相关函数参数的似然性，并确定了两种模式类型。I型模式的特征在于近似误差是块金的函数，因此可以变得任意小，有效地产生插值仿真器。类型II模式导致仿真器具有恒定的近似误差。除了从理论上调查的近似误差的限制，一个实用的方法，自动施加限制其程度。这是通过将惩罚项添加到似然函数中来实现的，并控制计算机模型中无法解释的变化量。主要研究结果说明了从能源平衡气候模式的数据。(C)2012爱思唯尔有限公司版权所有。
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. (C) 2012 Elsevier B.V. All rights reserved.