Development of the Likelihood Procedures for the Spatial Point Patterns and Their Applications

空间点模式似然程序的开发及其应用

• 批准号: 60530016
• 负责人: TANEMURA Masaharu
• 金额: $ 0.7万
• 依托单位: The Institute of Statistical Mathematics
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1985
• 资助国家: 日本
• 起止时间: 1985 至 1986
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-60530016/
• 关键词: 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

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.

在生态学、地理学、医学、材料工艺学、物理学、化学等应用科学的许多领域中，都需要对某些物体在平面或空间上的分布规律进行统计分析，在空间分布规律的统计分析和统计建模中，出现了不同于其他统计领域的新特点，难以用现行方法处理。因此，空间数据本身需要一种独创的方法。空间数据的基于似然性的方法当然是可取的，但直到现在它们还没有得到充分的发展，因为在许多情况下，在构造和实际计算似然函数的困难，几年前，我们已经实现了空间点模式的相互作用势估计的似然性方法，通过应用近似方法克服了困难。在这个研究项目中，我们的目标是发展我们的程序，适用于更广泛的空间模式和模型。因此，它成为可能的情况下，环境条件是不均匀的，以估计对象之间的相互作用潜力和环境的空间变化。此外，当排斥相互作用的预期，我们扩展了一组单独的一个参数的软核模型，一个单一的两个参数的软核模型，并有可能使用更广泛的模型类。在本项目期间，还进行了其他一些关于空间点模式的研究。还有许多问题尚未解决，包括在各自科学领域的应用，我们希望将其视为我们未来研究的主题。

项目成果

M.Tanemura: "Nearest Neighbour Distance Approach for the Analysis of Spatial Point Patterns" Biometrics [Research Memorandum No. 320, The Institute of Statistical Mathematics]. (1987)

M.Tanemura：“用于分析空间点模式的最近邻距离方法”生物识别[研究备忘录第 320 号，统计数学研究所]。

Y.Ogata: Proceedings of the XIIIth International Biometric Conference:Invited Papers,Seattle,Wasington,U.S.A.July 27-August 1,1986. 12.14-12.28 (1986)

Y.Ogata：第十三届国际生物识别会议论文集：特邀论文，西雅图，华盛顿，美国，1986 年 7 月 27 日至 8 月 1 日。

M.Tanemura: "On the Stereology of the Radial Distribution Function of Hard-Sphere Systems" Science on FORM :Proceedings of the First International Symposium for Science on Form (General ed.: S.Ishizaka), Reidel. 157-165 (1986)

M.Tanemura：“论硬球系统径向分布函数的体视学”《形式科学》：第一届国际形式科学研讨会论文集（总编：S.Ishizaka），Reidel。

M.Tanemura General Ed.:S.Ishizaka: Science on Form:Proceedings of the First International Symposium for Science on Form,KTK Scientific Publishers,Reidel. 157-165 (1986)

M.Tanemura 总编：S.Ishizaka：形式科学：第一届国际形式科学研讨会论文集，KTK 科学出版社，Reidel。

Y.Ogata: "The Likelihood Analysis for Spatial Point Patterns" Proceedings of the XIIIth International Biometric Conference: Invited Papers, Seattle, Washington, U.S.A. July 27-August 1, 1986. 12.14-12.28 (1986)

Y.Ogata：“空间点模式的可能性分析”第十三届国际生物识别会议论文集：特邀论文，美国华盛顿州西雅图，1986年7月27日至8月1日。12.14-12.28 (1986)