Statistical Analysis of Spatial Data

本项目的主要成果如下：吉本点过程作为空间数据统计模型基础的理论研究。特别是得到了非相交球尺寸分布的一般形式，这在立体学中具有重要意义；得到了配分函数的精细近似公式，这在势函数的极大似然估计中具有重要意义。计算机空间数据的图像和图形分析。特别是测试了一种与速度相关的Voronoi转换算法，并开发了一个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。重点讨论了反高斯分布与车辆速度分布的拟合问题。研究了统计的其他分支，如时间序列分析、渐近理论和序列分析的方法和概念的联系和适用性。实际数据的应用。特别进行了个体生长的统计分析和某一地区的流行病学研究。

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.