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Modern statistics for spatial point processes (with discussion). (English) Zbl 1157.62067

In this survey article the current state of spatial point processes statistical theory is discussed. Cox and Gibbs models of spatial processes are described. Exploratory and diagnostic tools based on the residuals of spatial process models are considered. Maximum likelihood and Bayesian inference with application of Markov chain Monte Carlo and perfect simulations are presented. Simulation free inference using various estimating functions is described. Many examples of real life data are presented. Special attention is paid to inhomogeneous models and computer intensive techniques.

MSC:

62M30 Inference from spatial processes
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62F15 Bayesian inference
65C40 Numerical analysis or methods applied to Markov chains

Software:

spatstat
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