Geometric anisotropic spatial point pattern analysis and Cox processes

Jesper Møller, Håkon Toftaker

Research output: Book/ReportReportResearch

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Abstract

We consider spatial point processes with a pair correlation function g(u) which depends only on the lag vector u between a pair of points. Our interest is in statistical models with a special kind of ‘structured’ anisotropy: g is geometric anisotropy if it is elliptical but not spherical.
In particular we study Cox process models with an elliptical pair correlation function, including shot noise Cox processes and log Gaussian Cox processes, and we develop estimation procedures using summary statistics and Bayesian methods. Our methodology is illustrated on real and synthetic datasets of spatial point patterns.

Original languageEnglish
PublisherDepartment of Mathematical Sciences, Aalborg University
Number of pages36
Publication statusPublished - Jan 2012
SeriesResearch Report Series
NumberR-2012-01
ISSN1399-2503

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Spatial Point Pattern
Cox Process
Pattern Analysis
Pair Correlation Function
Anisotropy
Shot Noise Process
Spatial Point Process
Cox Model
Bayesian Methods
Gaussian Process
Process Model
Statistical Model
Statistics
Methodology

Cite this

Møller, J., & Toftaker, H. (2012). Geometric anisotropic spatial point pattern analysis and Cox processes. Department of Mathematical Sciences, Aalborg University. Research Report Series, No. R-2012-01
Møller, Jesper ; Toftaker, Håkon. / Geometric anisotropic spatial point pattern analysis and Cox processes. Department of Mathematical Sciences, Aalborg University, 2012. 36 p. (Research Report Series; No. R-2012-01).
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Møller, J & Toftaker, H 2012, Geometric anisotropic spatial point pattern analysis and Cox processes. Research Report Series, no. R-2012-01, Department of Mathematical Sciences, Aalborg University.

Geometric anisotropic spatial point pattern analysis and Cox processes. / Møller, Jesper; Toftaker, Håkon.

Department of Mathematical Sciences, Aalborg University, 2012. 36 p.

Research output: Book/ReportReportResearch

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Møller J, Toftaker H. Geometric anisotropic spatial point pattern analysis and Cox processes. Department of Mathematical Sciences, Aalborg University, 2012. 36 p. (Research Report Series; No. R-2012-01).