Study of Geostatistical Predictions based on Block Data

在2006年的硕士论文《块状数据的克立格方法参数估计算法研究》中，我们提出了一种基于块状数据的地质统计预测的克立格方法，并提出了一种计算克立格极大似然估计的有效算法。在本研究中，块被限制为全等矩形。我们一直在尝试将所提出的算法扩展到更一般形式的块。但这需要计算大量的大型协方差矩阵，其中的每个元素都需要进行耗时的数值积分，不可避免地要进行分布式计算。我们一直在进行数值实验，希望在不久的将来发表结果。在硕士论文《关于协变量众多时的协克里格方法的研究》(2007，Usuda Kenji)中，我们考虑了协变量多的情况下的协克里格方法。在这种情况下，标准方法只使用协变量的一部分，以便于数值计算，并且肯定会丢弃包含某些信息的协变量。我们建议使用CAVARIATE被划分成的块，并使用块之间的协方差。本文所做的初步数值实验表明，我们的新方法比传统方法具有更好的性能。我们希望在不久的将来进行更多的实验后才能公布结果。此外，Mase还发布了开源统计系统System R的编程手册，该系统已成为全球通用的统计分析工作台。这本书有很好的口碑。

In the master thesis "On the study of an algorithm of parameter estimation for Kriging method for block data" (2006, Koji Takahashi), we proposed a Kriging method for geostatistical prediction based on block data and developed an efficient algorithm for calculating maximum likelihood estimators of Kriging. In this study, block are restricted to congruent rectangles. We have been trying to extend the proposed algorithm to block of more general forms. But this needs calculation of a lot of large covariance matrices Each elements of which needs a time-consuming numerical integrations and distributed computations are unavoidable. We have been carrying numerical experiments and hope the result will be published in near future.In the master thesis "On the study of cokrging method when there are numerous covariates" (2007, Kenji Usuda), we consider a cokriging method under the condition that there are numerous covariates. In this situation, a standard method uses only a part of covariates in order to ease numerical computations and certainly discards a certain information contained covariates. We proposed to use blocks into which cavariates are partitioned and use covariances between blocks. A preliminary numerical experiments done in the thesis, our new method shows a better performance than a traditional method. We hope to publish the results after more experiments in near future.Also Mase published a programming manual of the system R which is an open source statistical system which has become a common workbench of statistical analysis all over the world. The book has gotten a good reputation.