Likelihood Inference for Unions of Interacting Discs

DOI10.1111/j.1467-9469.2009.00660.xzbMath1226.60016OpenAlexW2170803293MaRDI QIDQ3103129

Jesper Møller, Kateřina Staňková Helisová

Publication date: 26 November 2011

Published in: Scandinavian Journal of Statistics (Search for Journal in Brave)

Full work available at URL: http://vbn.aau.dk/ws/files/16203470/R-2008-18.pdf

zbMATH Keywords

summary statisticsBoolean modeledge effectsgerm-grain modelquermass-interaction processrandom closed setspatial Markov propertyconnected component Markov processdisc processsimulation-based maximum likelihood

Mathematics Subject Classification ID

Inference from spatial processes (62M30) Geometric probability and stochastic geometry (60D05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (16)

Quermass-interaction process with convex compact grains. ⋮ Estimation of the Intensity Parameter of the Germ-Grain Quermass-Interaction Model when the Number of Germs is not Observed ⋮ Spatio-temporal model for a random set given by a union of interacting discs ⋮ A new construction of covariance functions for Gaussian random fields ⋮ A new definition of random set ⋮ Power diagrams and interaction processes for unions of discs ⋮ Hierarchical Bayesian modeling of marked non-homogeneous Poisson processes with finite mixtures and inclusion of covariate information ⋮ sppmix: Poisson point process modeling using normal mixture models ⋮ Modeling the growth of objects through a stochastic process of random sets ⋮ Dimension reduction in extended quermass-interaction process ⋮ On the use of particle Markov chain Monte Carlo in parameter estimation of space-time interacting discs ⋮ Assessing similarity of random sets via skeletons ⋮ Testing equality of distributions of random convex compact sets via theory of \(\mathfrak{N} \)-distances ⋮ Planar segment processes with reference mark distributions, modeling and estimation ⋮ Percolation results for the continuum random cluster model ⋮ Modelling the evolution of a random set utilizing covariate information with applications to nowcasting

Uses Software

• spatial

Cites Work

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• Random fields
• Densities for stationary random sets and point processes
• Power diagrams and interaction processes for unions of discs
• Markov connected component fields
• Markov interacting component processes
• Quermass-interaction processes: conditions for stability
• Markov properties of cluster processes
• Nearest-Neighbour Markov Point Processes and Random Sets
• Statistical Inference for Spatial Processes

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