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

Øivind Skare, Jesper Møller, Eva B. Vedel Jensen

Research output: Contribution to journalJournal articleResearchpeer-review

9 Citations (Scopus)

Abstract

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.
Original languageEnglish
JournalStatistics and Computing
Volume17
Issue number4
Pages (from-to)369-379
Number of pages11
ISSN0960-3174
DOIs
Publication statusPublished - 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

Cite this

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

In: Statistics and Computing, Vol. 17, No. 4, 2007, p. 369-379.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Bayesian analysis of spatial point processes in the neighbourhood of Voronoi networks

AU - Skare, Øivind

AU - Møller, Jesper

AU - Jensen, Eva B. Vedel

PY - 2007

Y1 - 2007

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.

U2 - 10.1007/s11222-007-9029-8

DO - 10.1007/s11222-007-9029-8

M3 - Journal article

VL - 17

SP - 369

EP - 379

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 4

ER -