Statistical Tests for Cross-Validation of Kriging Models
Statistical Tests for Cross-Validation of Kriging Models
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DOI：
10.2139/ssrn.3395872
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发表时间：
2019-05
期刊：
影响因子：
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通讯作者：
J. Kleijnen;W. V. Beers
中科院分区：
文献类型：
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作者：
J. Kleijnen;W. V. Beers
克里金或高斯过程模型是仿真模型的流行元模型(代理模型或仿真器)；这些元模型为未仿真的输入组合提供预测器。为了验证这些用于计算昂贵的模拟模型的元模型，分析人员通常应用计算高效的交叉验证。在这篇文章中，我们给出了所谓的留一交叉验证的新的统计检验。在图形上，我们将这些检验表示为散点图，这些散点图增加了使用克立格预报器的估计方差的置信度区间。为了估计这些预测因子的真实方差，我们可能会使用自举。像其他统计检验一样，我们的检验--无论有没有自举--都有I类和II类错误概率；为了估计这些概率，我们使用蒙特卡罗实验。我们也使用这样的实验来研究统计收敛。为了说明我们测试的应用，我们使用(I)具有两个输入的示例和(Ii)具有八个输入的流行的钻孔示例。投稿摘要：模拟模型在运筹学中非常流行，也被称为计算机模拟或计算机实验。一个流行的话题是计算机实验的设计和分析。本文重点研究了克立格法和交叉验证法在仿真模型中的应用，这些方法和模型是运筹学中常用的方法和模型。更具体地说，本文提供了以下内容：(1)用于留一交叉验证的新的统计检验的基本变体；(2)用于估计Kriging预报器的真方差的Bootstrap方法；以及(3)用于评估Kriging预报器的一致性的蒙特卡罗实验，用于评估学生化预测误差到标准正态变量的收敛，以及用于预期实验I类错误率到预先指定的标称值的收敛。通过实例说明了新的统计检验方法，包括流行的井眼模型。
Kriging or Gaussian process models are popular metamodels (surrogate models or emulators) of simulation models; these metamodels give predictors for input combinations that are not simulated. To validate these metamodels for computationally expensive simulation models, the analysts often apply computationally efficient cross-validation. In this paper, we derive new statistical tests for so-called leave-one-out cross-validation. Graphically, we present these tests as scatterplots augmented with confidence intervals that use the estimated variances of the Kriging predictors. To estimate the true variances of these predictors, we might use bootstrapping. Like other statistical tests, our tests—with or without bootstrapping—have type I and type II error probabilities; to estimate these probabilities, we use Monte Carlo experiments. We also use such experiments to investigate statistical convergence. To illustrate the application of our tests, we use (i) an example with two inputs and (ii) the popular borehole example with eight inputs. Summary of Contribution: Simulation models are very popular in operations research (OR) and are also known as computer simulations or computer experiments. A popular topic is design and analysis of computer experiments. This paper focuses on Kriging methods and cross-validation methods applied to simulation models; these methods and models are often applied in OR. More specifically, the paper provides the following; (1) the basic variant of a new statistical test for leave-one–out cross-validation; (2) a bootstrap method for the estimation of the true variance of the Kriging predictor; and (3) Monte Carlo experiments for the evaluation of the consistency of the Kriging predictor, the convergence of the Studentized prediction error to the standard normal variable, and the convergence of the expected experimentwise type I error rate to the prespecified nominal value. The new statistical test is illustrated through examples, including the popular borehole model.