Log Gaussian Cox processes on the sphere

Research output: Contribution to journalJournal articleResearchpeer-review

1 Citation (Scopus)

Abstract

log Gaussian Cox process (LGCP) is a doubly stochastic construction consisting of a Poisson point process with a random log-intensity given by a Gaussian random field. Statistical methodology have mainly been developed for LGCPs defined in the d-dimensional Euclidean space. This paper concerns the case of LGCPs on the d-dimensional sphere, with d=2 of primary interest. We discuss the existence problem of such LGCPs, provide sufficient existence conditions, and establish further useful theoretical properties. The results are applied for the description of sky positions of galaxies, in comparison with previous analysis based on a Thomas process, using simple estimation procedures and making a careful model checking. We account for inhomogeneity in our models, and as the model checking is based on a thinning procedure which produces homogeneous/isotropic LGCPs, we discuss its sensitivity.
Original languageEnglish
JournalSpatial Statistics
Volume26
Pages (from-to)69-82
Number of pages14
ISSN2211-6753
DOIs
Publication statusPublished - 2018

Fingerprint

Cox Process
Model checking
Gaussian Process
Model Checking
Poisson Point Process
Gaussian Random Field
Galaxies
Thinning
Inhomogeneity
Euclidean space
Sufficient
inhomogeneity
thinning
Methodology
methodology
Model

Keywords

  • Hölder continuity
  • Pair correlation function
  • point processes on the sphere
  • reduced Palm distribution
  • second order intensity reweighted homogeneity
  • Thinning procedure for model checking

Cite this

@article{128a5aee7c0f4947b41e332eee7fb1f4,
title = "Log Gaussian Cox processes on the sphere",
abstract = "log Gaussian Cox process (LGCP) is a doubly stochastic construction consisting of a Poisson point process with a random log-intensity given by a Gaussian random field. Statistical methodology have mainly been developed for LGCPs defined in the d-dimensional Euclidean space. This paper concerns the case of LGCPs on the d-dimensional sphere, with d=2 of primary interest. We discuss the existence problem of such LGCPs, provide sufficient existence conditions, and establish further useful theoretical properties. The results are applied for the description of sky positions of galaxies, in comparison with previous analysis based on a Thomas process, using simple estimation procedures and making a careful model checking. We account for inhomogeneity in our models, and as the model checking is based on a thinning procedure which produces homogeneous/isotropic LGCPs, we discuss its sensitivity.",
keywords = "H{\"o}lder continuity, Pair correlation function, point processes on the sphere, reduced Palm distribution, second order intensity reweighted homogeneity, Thinning procedure for model checking",
author = "Pacheco, {Francisco Andr{\'e}s Cuevas} and Jesper M{\o}ller",
year = "2018",
doi = "10.1016/j.spasta.2018.06.002",
language = "English",
volume = "26",
pages = "69--82",
journal = "Spatial Statistics",
issn = "2211-6753",
publisher = "Elsevier",

}

Log Gaussian Cox processes on the sphere. / Pacheco, Francisco Andrés Cuevas; Møller, Jesper.

In: Spatial Statistics, Vol. 26, 2018, p. 69-82.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Log Gaussian Cox processes on the sphere

AU - Pacheco, Francisco Andrés Cuevas

AU - Møller, Jesper

PY - 2018

Y1 - 2018

N2 - log Gaussian Cox process (LGCP) is a doubly stochastic construction consisting of a Poisson point process with a random log-intensity given by a Gaussian random field. Statistical methodology have mainly been developed for LGCPs defined in the d-dimensional Euclidean space. This paper concerns the case of LGCPs on the d-dimensional sphere, with d=2 of primary interest. We discuss the existence problem of such LGCPs, provide sufficient existence conditions, and establish further useful theoretical properties. The results are applied for the description of sky positions of galaxies, in comparison with previous analysis based on a Thomas process, using simple estimation procedures and making a careful model checking. We account for inhomogeneity in our models, and as the model checking is based on a thinning procedure which produces homogeneous/isotropic LGCPs, we discuss its sensitivity.

AB - log Gaussian Cox process (LGCP) is a doubly stochastic construction consisting of a Poisson point process with a random log-intensity given by a Gaussian random field. Statistical methodology have mainly been developed for LGCPs defined in the d-dimensional Euclidean space. This paper concerns the case of LGCPs on the d-dimensional sphere, with d=2 of primary interest. We discuss the existence problem of such LGCPs, provide sufficient existence conditions, and establish further useful theoretical properties. The results are applied for the description of sky positions of galaxies, in comparison with previous analysis based on a Thomas process, using simple estimation procedures and making a careful model checking. We account for inhomogeneity in our models, and as the model checking is based on a thinning procedure which produces homogeneous/isotropic LGCPs, we discuss its sensitivity.

KW - Hölder continuity

KW - Pair correlation function

KW - point processes on the sphere

KW - reduced Palm distribution

KW - second order intensity reweighted homogeneity

KW - Thinning procedure for model checking

U2 - 10.1016/j.spasta.2018.06.002

DO - 10.1016/j.spasta.2018.06.002

M3 - Journal article

VL - 26

SP - 69

EP - 82

JO - Spatial Statistics

JF - Spatial Statistics

SN - 2211-6753

ER -