ROBUST GAUSSIAN STOCHASTIC PROCESS EMULATION
ROBUST GAUSSIAN STOCHASTIC PROCESS EMULATION
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DOI：
10.1214/17-aos1648
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发表时间：
2018-12-01
影响因子：
4.5
通讯作者：
Berger, James O.
中科院分区：
文献类型：
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作者：
Gu, Mengyang;Wang, Xiaojing;Berger, James O.
在计算机模型的模拟(近似)的背景下，我们考虑了高斯随机过程(GAP)的参数估计，其结果是实值标量。主要集中在通过各种广义最大似然方法估计GAP参数，主要涉及寻找后验模式；这是因为计算机模型仿真中的完全贝叶斯分析通常代价高昂，所研究的后验模式来自客观先验，例如参考先验。这些先验已在文献中针对各向同性协方差函数的情况或在GAP构造中使用的模型运行的输入的设计中的可分离性假设下进行了研究。在本文中，我们考虑具有一类常用的各向异性相关函数的更一般的设计(例如，拉丁超立方体设计)，其可以表示为各向同性相关函数的乘积，每个各向同性相关函数具有未知的范围参数和固定的粗糙度参数。我们讨论了GAP参数的客观先验和边际似然的性质，并建立了GAP参数的后验适定性，但我们的主要重点是证明某些参数比其他参数的估计更稳健，并且一些常用的参数应该明确地被避免。这些结果适用于许多常用的协方差函数，如幂指数、Matn、有理二次和球面协方差等。我们还将结果推广到带有块金参数的GAP模型。关于所研究的程序的性能，给出了理论和数值证据。
We consider estimation of the parameters of a Gaussian Stochastic Process (GaSP), in the context of emulation (approximation) of computer models for which the outcomes are real-valued scalars. The main focus is on estimation of the GaSP parameters through various generalized maximum likelihood methods, mostly involving finding posterior modes; this is because full Bayesian analysis in computer model emulation is typically prohibitively expensive.The posterior modes that are studied arise from objective priors, such as the reference prior. These priors have been studied in the literature for the situation of an isotropic covariance function or under the assumption of separability in the design of inputs for model runs used in the GaSP construction. In this paper, we consider more general designs (e.g., a Latin Hypercube Design) with a class of commonly used anisotropic correlation functions, which can be written as a product of isotropic correlation functions, each having an unknown range parameter and a fixed roughness parameter. We discuss properties of the objective priors and marginal likelihoods for the parameters of the GaSP and establish the posterior propriety of the GaSP parameters, but our main focus is to demonstrate that certain parameterizations result in more robust estimation of the GaSP parameters than others, and that some parameterizations that are in common use should clearly be avoided. These results are applicable to many frequently used covariance functions, for example, power exponential, Matern, rational quadratic and spherical covariance. We also generalize the results to the GaSP model with a nugget parameter. Both theoretical and numerical evidence is presented concerning the performance of the studied procedures.