Statistical Model of Mutually Non-intersecting Systems of Balls with High Intensity and Its Application to Environmental Sciences

(1)相互不相交的高强度球系模型在空间统计学中具有重要意义。我们研究了利用硬核Gibbsian点过程构造这类过程的可能性，并证明了以下重要性质。“这种点过程的强度可以接近空间的最接近堆积密度”。这一结果表明，使用硬核Gibbsian点过程可以得到任意可能的高强度模型。模拟回火方法能够高强度地模拟这类过程。研究结果已提交给统计期刊《神经》。安装统计数据。数学课。最大伪似然法是估计Gibbsian点过程参数的统计方法。证明了它们的渐近统计性质，证明了它们的相合性和渐近正态。研究结果发表在德国数学期刊《数学》上。(3)空间统计在日本仍然鲜为人知。Mase写了日本第一本关于空间统计的书，将这个领域介绍给日本。在这本书中，解释了吉伯斯点过程的基础知识及其模拟方法。这本书将于2000年由共同社出版。

(1) Models of mutually non-intersecting systems of balls with high intensity are important in spatial statistics. We studied the possibility of constructiong such processes using hard-core Gibbsian point processes and proved the following important property. "The intensity of such point processes can be as close as to the closest packing density of the space". This result shows that we can get models of arbitrary possible high intensity using hard-core Gibbsian point processes. Also we showed that the simulated tempering method is capable to simulate such processes with high intensity. The result has been to submitted to the statistical journal Ann. Inst. Statis. Math. and is now under revision.(2) Maximum pseudo-likelihood method is the statistical procedure to estimate parameters of Gibbsian point processes. We proved their asymptotic statistical properties and proved their consistency and asymptotic normality. Result were published in German mathematical journal Math. Nach.(3) Spatial statistics is still less known in Japan. Mase wrote a first book on Spatial statistics in Japan to introduce this field to Japan. In this book, basics of Gibbsian point processes and their simulation methods are explained. The book will be published in 2000 from Kyoritsu Publishing Co.