Development of the Likelihood Procedures for the Spatial Point Patterns and Their Applications
| Project/Area Number |
60530016
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
統計学
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
TANEMURA Masaharu (1986) Associate Professor, The Institute of Statistical Mathematics, その他, 助教授 (80000214)
稲村 正美 (1985) 統計数理研究所
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| Co-Investigator(Kenkyū-buntansha) |
OGATA Yosihiko Associate Professor, The Institute of Statistical Mathematics, 統計基礎研究系, 助教授 (70000213)
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| Project Period (FY) |
1985 – 1986
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| Project Status |
Completed (Fiscal Year 1986)
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| Budget Amount *help |
¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1986: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 1985: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | Spatial data / Interaction potential / Soft-core model / Spatial variation of environment / Ecology / Gibbsian likelihood / Nearest neighbour distance / マーク付き点過程 |
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| Research Abstract |
For the patterns of certain objects which are distributed in the plane or in the space, there are requirements to analyse them statistically in many fields of applied science such as ecology, geography, medicine, material technology, physics, chemistry and so on. In the statistical analysis and statistical modelling of spatial patterns, there appear new features which are different from those in the other fields of statistics and which are difficult to manage by the prevailing methods. Thus, spatial data need an original methodology for its own. The likelihood-based procedures for spatial data will be of course desirable, but until now they are not sufficiently developed because of the difficulties in constructing and in practically computing likelihood functions in many cases.
Several years ago, we have realized likelihood procedure for estimating interaction potentials of spatial point patterns, by overcoming the difficulty through an application of approximation methods. In this research project, we aimed at developing our procedure to be applicable for wider classes of spatial patterns and models. As a result, it became possible, in case the condition of environment is inhomogeneous, to estimate both the interaction potential between objects and the spatial variation of environment. Moreover, when repulsive interactions are expected, we extended a set of individual one-parameter soft-core models to a single two-parameter soft-core model and made possible to use wider class of models. Several other researches concerning spatial point patterns were also done during the period of this project. There are many problems untached including the application to respective fileds of science, and we hope to consider them to be the future themes of our research.
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Report
(1 results)
Research Products
(8 results)
