Study of Geostatistical Predictions based on Block Data

在硕士论文《关于块数据Kriging方法参数估计算法的研究》（2006，高桥浩二）中，我们提出了一种基于块数据的地质统计预测Kriging方法，并开发了一种计算Kriging极大似然估计量的高效算法。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协方差矩阵，其中每个元素都需要耗费大量的时间进行数值积分和分布式计算。我们一直在进行数值实验，希望结果能在不久的将来发表。在硕士论文《关于多协变量条件下的协克里格方法研究》（2007,Kenji Usuda）中，我们考虑了多协变量条件下的协克里格方法。在这种情况下，为了简化数值计算，标准方法只使用部分协变量，当然会丢弃某些包含协变量的信息。我们建议使用将变量划分成的块，并使用块之间的协方差。初步的数值实验表明，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发表结果。此外，Mase还发布了R系统的编程手册，R系统是一个开源的统计系统，已经成为全世界统计分析的通用工作台。这本书获得了很好的声誉。

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.