Statistical Inference on Spatial Random Network

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In the field of "Spatial Statistics", the research of the parametric methods for clustered point patterns (namely, the point patterns with inhomogeneity) had been insufficient. In order to break the above status, we started to study the spatial point patterns which are assumed to be generated from the random network structures as one of the classes of inhomogeneous point patterns. Our purposes were to construct the models of spatial statistics corresponding to the above assumption, to develop a method of parametric estimating and to confirm the validity of both the model and the method. Our final object was to apply our model and method to the observed real data.As a possible parametric method, we proposed the following approach based on Bayesian procedure. Let us assume that the observed data is represendted by the configuration of points x and that the data was ocurred from the boundaries of, say, polycrystalline network in three-dimensional space. There is surely the case our assump … More tions are realistic. Let y be the unobserved generating points of the netowrk. Furthermore, we assume, on the edge of the network, the unobserved point z which has one to one correspondence to each observation x such that x=z+ε. Here we assume that ε obeys the normal distribution. Finally we suppose that the network which is generated through y is composed of Voronoi tessellation network. Under the suitable prior distributions of unobserved variables, we used Markov Chain Monte Carlo (MCMC) method for obtaining the posterior distributions.We have confirmed that our procedure is valid for the two-dimensional artificial data which was produced by computer simulation. At this stage, our results are presented at the International Conference which was held in Canada in 1999 and so on. At the same time, we prepared the publication of the FORTRAN programs wich were devised for the dynamic construction of Voronoi tessellation in two dimensions.Certain results are already published and some results are under the preparation for publication. Less