Statistical Analysis of Spatial Data

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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.