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Likelihood analysis of spatial point patterns. (English) Zbl 0579.62087
Summary: The likelihood procedure for estimating the pairwise interaction potential function is developed for statistical analysis of homogeneous spatial point patterns. Approximation methods of the normalizing factor of Gibbs canonical distribution are discussed both to estimate a scale parameter and to measure the softness (or hardness) of repulsive interactions. The approximations are useful up to a considerably high density. The validity of our procedure is demonstrated by some computer experiments. Some real data are analysed.
MSC:
62M99Inference from stochastic processes
60K35Interacting random processes; statistical mechanics type models; percolation theory
62P99Applications of statistics