Titlebook: Case Studies in Spatial Point Process Modeling; Adrian Baddeley,Pablo Gregori,Dietrich Stoyan Book 2006 Springer-Verlag New York 2006 Bran

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https://doi.org/10.1007/0-387-31144-0Branching process; Markov property; Poisson process; point process; principal component analysis; statist

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978-0-387-28311-1Springer-Verlag New York 2006

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Progress in Theoretical Computer Sciencedemonstrate how the martingale technique applies to establish the analogues of the classical results: Doob’s theorem, Wald identity in this multi-dimensional setting. In particular, we show that the famous Slivnyak-Mecke theorem characterising the Poisson process is a consequence of the strong Markov property.

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Strong Markov Property of Poisson Processes and Slivnyak Formulademonstrate how the martingale technique applies to establish the analogues of the classical results: Doob’s theorem, Wald identity in this multi-dimensional setting. In particular, we show that the famous Slivnyak-Mecke theorem characterising the Poisson process is a consequence of the strong Markov property.

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Bayesian Analysis of Markov Point Processeslihood function is only specified up to a normalising constant. We illustrate the method in the setting of Bayesian inference for Markov point processes; more specifically we consider a likelihood function given by a Strauss point process with priors imposed on the unknown parameters. The method rel

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Statistics for Locally Scaled Point Processesodifications of homogeneous template point processes and have the property that regions with different intensity differ only by a location dependent scale factor. The main emphasis of the present paper is on analysis of such models. Statistical methods are developed for estimation of scaling functio