Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1984 · 138 citations · 26 references
ComputingBiostatisticsSpatial AnalysisSpatial Data AnalysisSpatial StatisticsPoint Pattern AnalysisPoint ProcessesSpatial Point ProcessesSpatial Random FieldsSpatial Statistical ModelingGibbs DistributionInteracting Point ProcessesInteraction FunctionsLikelihood AnalysisLikelihood EquationsPairwise Interaction PotentialsPairwise Interaction TermsRepulsive Point Processes
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.
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Equation of State Calculations by Fast Computing Machines
N. Metropolis, Arianna W. Rosenbluth, M. N. Rosenbluth et al. · The Journal of Chemical Physics · 1953 · 37.1K citations