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

高强度球互不相交系统统计模型及其在环境科学中的应用

基本信息

批准号：
10640106
负责人：
MASE Shigeru
金额：
$ 1.15万
依托单位：
Tokyo Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

项目摘要

(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.

(1)高强度球系统的互不相交模型是空间统计学中的一个重要问题。我们研究了用硬核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的堆积密度”。这一结果表明，我们可以得到任意可能的高强度使用硬核吉布斯点过程的模型。我们还表明，模拟回火方法能够以高强度模拟此类过程。结果已提交给统计杂志Ann.Inst.Statis。数学，现在正在复习中。(2)极大似然法是估计吉布斯点过程参数的统计方法。我们证明了它们的渐近统计性质，并证明了它们的相合性和渐近正态性。结果发表在德国数学杂志Math.Nach上。(3)空间统计学在日本仍然鲜为人知。Mase写了第一本书空间统计在日本介绍这一领域的日本。在这本书中，吉布斯点过程的基础知识和他们的模拟方法进行了解释。该书将于2000年由共立出版社出版。