Statistical Analysis of Spatial Data

本课题的主要研究成果如下：1.以吉布斯点过程为基础的空间数据统计模型的理论研究。特别是得到了在体视学中具有重要意义的不相交球体的尺寸分布的一般形式，以及对于势函数的最大似然估计具有重要意义的配分函数的更精细近似公式。在计算机上对空间数据进行图像和图形分析。特别是对绘制速度相关的Voronoi流苏算法进行了测试，并开发了Fortran图形工具程序包。与空间数据分析相关的组合和设计问题。重点讨论了空间数据的采样问题。交通流量分析。重点讨论了逆高斯分布对车速分布的拟合问题。研究了时间序列分析、渐近理论和序列分析等统计学其他分支的方法和概念之间的联系和适用性。对实际数据的应用。特别是对某地区的个体生长情况进行了统计分析和流行病学研究。

Main results of this project are classified as follows:1. Theoretical studies of Gibbsian point processes as a basis of the statistical model of spatial data. Especially a general form of size distributions for non-intersecting balls which is important in stereology and a finer approximation formula for partition functions which is important for maximum likelihood estimation of potential functions are obtained.2. Image and Graphical analysis of spatial data on computers. Especially an algorithm of drawing speed-dependent Voronoi tasselations was tested and a program package for graphical tools of Fortran was developed.3. Combinatorial and Design problems associated with spatial data analysis. Especially a sampling problem of spatial data was discussed.4. Analysis of traffic flows. Especially a fitting problem of inverse Gaussian distributions to speed distributions of vehicles was discussed.5. The connection and the applicability of methods and concepts of other branches of statistics, e.g. timeseries analysis, asymptotic theory and sequential analysis, were studies.6. Applications to practical data. Especially a statistical analysis of individual growth and epidemical studies in a district were undertaken.