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Including a Nugget Effect in Lifted Brownian Covariance Models
SIAM/ASA Journal on Uncertainty Quantification ( IF 2 ) Pub Date : 2020-10-22 , DOI: 10.1137/19m1255252
Yang Yu , Ning Zhang , Daniel W. Apley , Wenxin Jiang

SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 4, Page 1338-1357, January 2020.
Kriging is widely used for modeling the response surface in computer simulations in science and engineering. A Brownian integrated (BI) covariance model and its variant, the lifted Brownian (LB) covariance model, were recently proposed as the underlying random field models for kriging, and they were shown to have attractive properties for modeling deterministic computer experiment data. With no nugget effect, kriging models will perfectly interpolate the response data, which is usually desirable for deterministic simulations. However, it is necessary to include a nugget effect when modeling stochastic simulations or when combining simulation with physical experimental data, and inclusion of a nugget effect is often beneficial, even with deterministic simulations, to avoid numerical problems. This is challenging for the LB covariance, which requires translation based on a perfectly observed response value. In this paper, we introduce a novel approach for including a nugget effect in LB covariance models in a manner that preserves their desirable properties. We also derive a number of important theoretical results, including invariance to the choice of translation point and Bayesian connections.


中文翻译:

在提升布朗协方差模型中包括金块效应

SIAM / ASA不确定性量化期刊,第8卷,第4期,第1338-1357页,2020年1月。
Kriging被广泛用于在科学和工程学中的计算机仿真中对响应面进行建模。最近,人们提出了布朗综合(BI)协方差模型及其变体,即提升布朗(LB)协方差模型,作为克里金法的基础随机场模型,并被证明具有为确定性计算机实验数据建模的诱人特性。在没有块效应的情况下,克里金模型将完美地插值响应数据,这对于确定性仿真通常是理想的。但是,在对随机模拟进行建模或将模拟与物理实验数据结合在一起时,有必要包括块金效应,并且即使没有确定性模拟,包含块金效应通常也是有益的,以避免数值问题。对于LB协方差来说,这是一个挑战,这需要根据完美观察到的响应值进行转换。在本文中,我们介绍了一种新颖的方法,该方法以保留其理想属性的方式在LB协方差模型中包含块金效应。我们还得出了许多重要的理论结果,包括不变地选择了翻译点和贝叶斯联系。
更新日期:2020-12-06
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