Fifty Years of Kriging
Fifty Years of Kriging
复制标题
DOI：
10.1007/978-3-319-78999-6_29
复制
发表时间：
2018-01-01
期刊：
影响因子：
--
通讯作者：
Desassis, Nicolas
中科院分区：
文献类型：
--
作者：
Chiles, Jean-Paul;Desassis, Nicolas
随机函数模型和克里金法构成了Georges Matheron在20世纪60年代创建的地质统计学方法的核心，并在他于1968年在枫丹白露巴黎矿业学院创建的研究中心得到了进一步发展。克里金法最初是为了避免在估计采矿区的平均品位时出现偏差而开发的，后来逐步应用于自然资源评估和地球科学的所有领域，最近又应用于全新的领域，例如计算机实验的设计和分析（DACE）。虽然克里金法的基本理论相当简单，但其在各种情况下的应用需要扩展所考虑的随机函数模型和实际问题的合理解决方案。本章介绍了克里金法的起源以及它的理论和应用沿着过去五十年的发展。更多的细节，目前正在开发的方法，以有效地处理克里金法的情况下，大量的数据和非平稳行为，特别是高斯马尔可夫随机场（GMRF）近似和随机偏微分（SPDE）的方法，与合成的情况下，后者的研究。
Random function models and kriging constitute the core of the geostatistical methods created by Georges Matheron in the 1960s and further developed at the research center he created in 1968 at Ecole des Mines de Paris, Fontainebleau. Initially developed to avoid bias in the estimation of the average grade of mining panels delimited for their exploitation, kriging received progressively applications in all domains of natural resources evaluation and earth sciences, and more recently in completely new domains, for example, the design and analysis of computer experiments (DACE). While the basic theory of kriging is rather straightforward, its application to a large diversity of situations requires extensions of the random function models considered and sound solutions to practical problems. This chapter presents the origins of kriging as well as the development of its theory and its applications along the last fifty years. More details are given for methods presently in development to efficiently handle kriging in situations with a large number of data and a nonstationary behavior, notably the Gaussian Markov random field (GMRF) approximation and the stochastic partial differential (SPDE) approach, with a synthetic case study concerning the latter.