Detecting dependence between marks and locations of marked point processes

Martin Schlather; Paulo J. Ribeiro; Peter J. Diggle

doi:10.1046/j.1369-7412.2003.05343.x

Detecting dependence between marks and locations of marked point processes

Martin Schlather, Paulo J. Ribeiro, Peter J. Diggle

Research output: Contribution to journal › Article › peer-review

72 Scopus citations

Abstract

We introduce two characteristics for stationary and isotropic marked point processes, E(h) and V(h), and describe their use in investigating mark-point interactions. These quantities are functions of the interpoint distance h and denote the conditional expectation and the conditional variance of a mark respectively, given that there is a further point of the process a distance h away. We present tests based on E and V for the hypothesis that the values of the marks can be modelled by a random field which is independent of the unmarked point process. We apply the methods to two data sets in forestry.

Original language	English (US)
Pages (from-to)	79-93
Number of pages	15
Journal	Journal of the Royal Statistical Society. Series B: Statistical Methodology
Volume	66
Issue number	1
DOIs	https://doi.org/10.1046/j.1369-7412.2003.05343.x
State	Published - 2004
Externally published	Yes

Keywords

Independence test
Mark correlation function
Mark variogram
Nearest neighbour
Preferential sampling
Random-field model

ASJC Scopus subject areas

General Mathematics
Statistics and Probability

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10.1046/j.1369-7412.2003.05343.x

Cite this

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AU - Ribeiro, Paulo J.

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AB - We introduce two characteristics for stationary and isotropic marked point processes, E(h) and V(h), and describe their use in investigating mark-point interactions. These quantities are functions of the interpoint distance h and denote the conditional expectation and the conditional variance of a mark respectively, given that there is a further point of the process a distance h away. We present tests based on E and V for the hypothesis that the values of the marks can be modelled by a random field which is independent of the unmarked point process. We apply the methods to two data sets in forestry.

KW - Independence test

KW - Mark correlation function

KW - Mark variogram

KW - Nearest neighbour

KW - Preferential sampling

KW - Random-field model

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Detecting dependence between marks and locations of marked point processes

Abstract

Keywords

ASJC Scopus subject areas

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