Study of Geostatistical Predictions based on Block Data

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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.