Summary statistics for inhomogeneous marked point processes

O. Cronie; M.N.M. van Lieshout

doi:10.1007/s10463-015-0515-z

Summary statistics for inhomogeneous marked point processes

O. Cronie, M.N.M. van Lieshout^*

^*Corresponding author for this work

Stochastic Operations Research

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

23 Citations (Scopus)

47 Downloads (Pure)

Abstract

We propose new summary statistics for intensity-reweighted moment stationary marked point processes with particular emphasis on discrete marks. The new statistics are based on the $n$-point correlation functions and reduce to cross $J$- and $D$-functions when stationarity holds. We explore the relationships between the various functions and discuss their explicit forms under specific model assumptions. We derive ratio-unbiased minus sampling estimators for our statistics and illustrate their use on a data set of wildfires.

Original language	English
Pages (from-to)	905-928
Number of pages	24
Journal	Annals of the Institute of Statistical Mathematics
Volume	68
Issue number	4
DOIs	https://doi.org/10.1007/s10463-015-0515-z
Publication status	Published - Aug 2016

Keywords

MSC-60D05
MSC-60G55
Marked point process
Nearest neighbour distance distribution function
Generating functional
Multivariate point process
Intensity-reweighted moment stationarity
Reduced Palm measure
$J$-function
$n$-point correlation function
2023 OA procedure

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10.1007/s10463-015-0515-z

ArticleFinal published version, 455 KBLicence: Taverne

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title = "Summary statistics for inhomogeneous marked point processes",

abstract = "We propose new summary statistics for intensity-reweighted moment stationary marked point processes with particular emphasis on discrete marks. The new statistics are based on the \$n\$-point correlation functions and reduce to cross \$J\$- and \$D\$-functions when stationarity holds. We explore the relationships between the various functions and discuss their explicit forms under specific model assumptions. We derive ratio-unbiased minus sampling estimators for our statistics and illustrate their use on a data set of wildfires.",

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note = "eemcs-eprint-26224 ",

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language = "English",

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journal = "Annals of the Institute of Statistical Mathematics",

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T1 - Summary statistics for inhomogeneous marked point processes

AU - Cronie, O.

AU - van Lieshout, M.N.M.

N1 - eemcs-eprint-26224

PY - 2016/8

Y1 - 2016/8

N2 - We propose new summary statistics for intensity-reweighted moment stationary marked point processes with particular emphasis on discrete marks. The new statistics are based on the $n$-point correlation functions and reduce to cross $J$- and $D$-functions when stationarity holds. We explore the relationships between the various functions and discuss their explicit forms under specific model assumptions. We derive ratio-unbiased minus sampling estimators for our statistics and illustrate their use on a data set of wildfires.

AB - We propose new summary statistics for intensity-reweighted moment stationary marked point processes with particular emphasis on discrete marks. The new statistics are based on the $n$-point correlation functions and reduce to cross $J$- and $D$-functions when stationarity holds. We explore the relationships between the various functions and discuss their explicit forms under specific model assumptions. We derive ratio-unbiased minus sampling estimators for our statistics and illustrate their use on a data set of wildfires.

KW - MSC-60D05

KW - MSC-60G55

KW - Marked point process

KW - Nearest neighbour distance distribution function

KW - Generating functional

KW - Multivariate point process

KW - Intensity-reweighted moment stationarity

KW - Reduced Palm measure

KW - $J$-function

KW - $n$-point correlation function

KW - 2023 OA procedure

U2 - 10.1007/s10463-015-0515-z

DO - 10.1007/s10463-015-0515-z

M3 - Article

SN - 0020-3157

VL - 68

SP - 905

EP - 928

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

IS - 4

ER -

Summary statistics for inhomogeneous marked point processes

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Keywords

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