论文标题
一些双变量cokriging模型的最佳设计
Optimal designs for some bivariate cokriging models
论文作者
论文摘要
本文重点介绍了双变量相交的Cokriging实验的估计和设计方面。对于一大批协方差矩阵，确定了线性依赖性标准，该标准允许双变量共处的Cokriging设置中的主要变量的最佳线性无偏估计器，以减少单变量的Kriging估计量。确定具有一维输入的简单和普通降低的Cokriging模型的有效预测的精确最佳设计。通过最小化最大值和集成的预测方差来找到设计，其中主要变量是Ornstein-uhlenbeck过程。对于具有已知协方差参数的简单和普通的Cokriging模型，均值设计对于这两个标准函数都是最佳的。未知协方差参数的更现实的方案是通过在参数向量上的先验分布来解决的，从而采用了贝叶斯方法来解决设计问题。事实证明，均值设计是两个标准的贝叶斯最佳设计。这项工作是通过为印度河设计最佳水监测系统而进行的。
This article focuses on the estimation and design aspects of a bivariate collocated cokriging experiment. For a large class of covariance matrices, a linear dependency criterion is identified, which allows the best linear unbiased estimator of the primary variable in a bivariate collocated cokriging setup to reduce to a univariate kriging estimator. Exact optimal designs for efficient prediction for such simple and ordinary reduced cokriging models with one-dimensional inputs are determined. Designs are found by minimizing the maximum and the integrated prediction variance, where the primary variable is an Ornstein-Uhlenbeck process. For simple and ordinary cokriging models with known covariance parameters, the equispaced design is shown to be optimal for both criterion functions. The more realistic scenario of unknown covariance parameters is addressed by assuming prior distributions on the parameter vector, thus adopting a Bayesian approach to the design problem. The equispaced design is proved to be the Bayesian optimal design for both criteria. The work is motivated by designing an optimal water monitoring system for an Indian river.
