1999 Fiscal Year Final Research Report Summary
Statistical Model of Mutually Non-intersecting Systems of Balls with High Intensity and Its Application to Environmental Sciences
| Project/Area Number |
10640106
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
MASE Shigeru Tokyo Institute of Technology, Department of Mathematical and Computing Sciences, Professor, 大学院・情報理工学研究科, 教授 (70108190)
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| Co-Investigator(Kenkyū-buntansha) |
FUJISAWA Hironori Tokyo Institute of Technology, Department of Mathematical and Computing Sciences, Research Associate, 大学院・情報理工学研究科, 助手 (00301177)
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| Project Period (FY) |
1998 – 1999
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| Keywords | hard-core / Gibbsian model / intensity / closest packing density / simulated tempering / pseudo-likelihood / spatial statistics / asymptotics |
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| Research Abstract |
(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.
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