Detecting dependence between marks and locations of marked point processes

Martin Schlather; Paulo J. Ribeiro; Peter 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 Diggle

Research output: Contribution to journal › Review article › peer-review

98 Citations (Scopus)

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
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
Publication status	Published - 1 Jan 2004
Externally published	Yes

Keywords

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

Access to Document

10.1046/j.1369-7412.2003.05343.x

Cite this

@article{fadf72d6809a4f9a9ed7827dc26a43af,

title = "Detecting dependence between marks and locations of marked point processes",

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.",

keywords = "Independence test, Mark correlation function, Mark variogram, Nearest neighbour, Preferential sampling, Random-field model",

author = "Martin Schlather and Ribeiro, \{Paulo J.\} and Peter Diggle",

year = "2004",

month = jan,

day = "1",

doi = "10.1046/j.1369-7412.2003.05343.x",

language = "English",

volume = "66",

pages = "79--93",

journal = "Journal of the Royal Statistical Society. Series B: Statistical Methodology",

issn = "1369-7412",

publisher = "Oxford University Press",

number = "1",

}

TY - JOUR

T1 - Detecting dependence between marks and locations of marked point processes

AU - Schlather, Martin

AU - Ribeiro, Paulo J.

AU - Diggle, Peter

PY - 2004/1/1

Y1 - 2004/1/1

N2 - 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.

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

U2 - 10.1046/j.1369-7412.2003.05343.x

DO - 10.1046/j.1369-7412.2003.05343.x

M3 - Review article

SN - 1369-7412

VL - 66

SP - 79

EP - 93

JO - Journal of the Royal Statistical Society. Series B: Statistical Methodology

JF - Journal of the Royal Statistical Society. Series B: Statistical Methodology

IS - 1

ER -

Detecting dependence between marks and locations of marked point processes

Abstract

Keywords

Access to Document

Fingerprint

Cite this