Decomposition of variance for spatial Cox processes

Abdollah Jalilian, Yongtao Guan, Rasmus Waagepetersen

Research output: Book/ReportReportResearch

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Abstract

Spatial Cox point processes is a natural framework for quantifying the various
sources of variation governing the spatial distribution of rain forest trees. We introducea general criterion for variance decomposition for spatial Cox processes and apply it to specific Cox process models with additive or log linear random intensity functions. We moreover consider a new and flexible class of pair correlation function models given in terms of Mat´ern covariance functions. The proposed methodology is applied to point pattern data sets of locations of tropical rain forest trees.
Original languageEnglish
PublisherDepartment of Mathematical Sciences, Aalborg University
Number of pages18
Publication statusPublished - Feb 2011
SeriesResearch Report Series
NumberR-2011-05
ISSN1399-2503

Fingerprint

decomposition
spatial distribution
methodology
rain forest
additive
tropical rain forest

Keywords

  • additive random intensity
  • composite likelihood
  • Cox process
  • Matérn covariance function
  • pair correlation function
  • variance component

Cite this

Jalilian, A., Guan, Y., & Waagepetersen, R. (2011). Decomposition of variance for spatial Cox processes. Department of Mathematical Sciences, Aalborg University. Research Report Series, No. R-2011-05
Jalilian, Abdollah ; Guan, Yongtao ; Waagepetersen, Rasmus. / Decomposition of variance for spatial Cox processes. Department of Mathematical Sciences, Aalborg University, 2011. 18 p. (Research Report Series; No. R-2011-05).
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Jalilian, A, Guan, Y & Waagepetersen, R 2011, Decomposition of variance for spatial Cox processes. Research Report Series, no. R-2011-05, Department of Mathematical Sciences, Aalborg University.

Decomposition of variance for spatial Cox processes. / Jalilian, Abdollah; Guan, Yongtao; Waagepetersen, Rasmus.

Department of Mathematical Sciences, Aalborg University, 2011. 18 p.

Research output: Book/ReportReportResearch

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AU - Waagepetersen, Rasmus

PY - 2011/2

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N2 - Spatial Cox point processes is a natural framework for quantifying the various sources of variation governing the spatial distribution of rain forest trees. We introducea general criterion for variance decomposition for spatial Cox processes and apply it to specific Cox process models with additive or log linear random intensity functions. We moreover consider a new and flexible class of pair correlation function models given in terms of Mat´ern covariance functions. The proposed methodology is applied to point pattern data sets of locations of tropical rain forest trees.

AB - Spatial Cox point processes is a natural framework for quantifying the various sources of variation governing the spatial distribution of rain forest trees. We introducea general criterion for variance decomposition for spatial Cox processes and apply it to specific Cox process models with additive or log linear random intensity functions. We moreover consider a new and flexible class of pair correlation function models given in terms of Mat´ern covariance functions. The proposed methodology is applied to point pattern data sets of locations of tropical rain forest trees.

KW - additive random intensity

KW - composite likelihood

KW - Cox process

KW - Matérn covariance function

KW - pair correlation function

KW - variance component

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Jalilian A, Guan Y, Waagepetersen R. Decomposition of variance for spatial Cox processes. Department of Mathematical Sciences, Aalborg University, 2011. 18 p. (Research Report Series; No. R-2011-05).