Bayesian analysis of spatial point processes in the neighbourhood of Voronoi networks

Øivind Skare, Jesper Møller, Eva B. Vedel Jensen

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

9 Citationer (Scopus)

Resumé

A model for an inhomogeneous Poisson process with high intensity near the edges of a Voronoi tessellation in 2D or 3D is proposed. The model is analysed in a Bayesian setting with priors on nuclei of the Voronoi tessellation and other model parameters. An MCMC algorithm is constructed to sample from the posterior, which contains information about the unobserved Voronoi tessellation and the model parameters. A major element of the MCMC algorithm is the reconstruction of the Voronoi tessellation after a proposed local change of the tessellation. A simulation study and examples of applications from biology (animal territories) and material science (alumina grain structure) are presented.
Udgivelsesdato: DEC
OriginalsprogEngelsk
TidsskriftStatistics and Computing
Vol/bind17
Udgave nummer4
Sider (fra-til)369-379
Antal sider11
ISSN0960-3174
DOI
StatusUdgivet - 2007

Fingerprint

Spatial Point Process
Voronoi Tessellation
Voronoi
Bayesian Analysis
MCMC Algorithm
Inhomogeneous Poisson Process
Materials Science
Tessellation
Alumina
Crystal microstructure
Materials science
Model
Nucleus
Biology
Animals
Simulation Study
Point process
Bayesian analysis
Markov chain Monte Carlo

Citer dette

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Bayesian analysis of spatial point processes in the neighbourhood of Voronoi networks. / Skare, Øivind; Møller, Jesper; Jensen, Eva B. Vedel.

I: Statistics and Computing, Bind 17, Nr. 4, 2007, s. 369-379.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

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AU - Møller, Jesper

AU - Jensen, Eva B. Vedel

PY - 2007

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N2 - A model for an inhomogeneous Poisson process with high intensity near the edges of a Voronoi tessellation in 2D or 3D is proposed. The model is analysed in a Bayesian setting with priors on nuclei of the Voronoi tessellation and other model parameters. An MCMC algorithm is constructed to sample from the posterior, which contains information about the unobserved Voronoi tessellation and the model parameters. A major element of the MCMC algorithm is the reconstruction of the Voronoi tessellation after a proposed local change of the tessellation. A simulation study and examples of applications from biology (animal territories) and material science (alumina grain structure) are presented.

AB - A model for an inhomogeneous Poisson process with high intensity near the edges of a Voronoi tessellation in 2D or 3D is proposed. The model is analysed in a Bayesian setting with priors on nuclei of the Voronoi tessellation and other model parameters. An MCMC algorithm is constructed to sample from the posterior, which contains information about the unobserved Voronoi tessellation and the model parameters. A major element of the MCMC algorithm is the reconstruction of the Voronoi tessellation after a proposed local change of the tessellation. A simulation study and examples of applications from biology (animal territories) and material science (alumina grain structure) are presented.

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