TY - JOUR
T1 - Log Gaussian Cox processes on the sphere
AU - Pacheco, Francisco Andrés Cuevas
AU - Møller, Jesper
PY - 2018
Y1 - 2018
N2 - A 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 - A 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
UR - http://www.scopus.com/inward/record.url?scp=85049340286&partnerID=8YFLogxK
U2 - 10.1016/j.spasta.2018.06.002
DO - 10.1016/j.spasta.2018.06.002
M3 - Journal article
SN - 2211-6753
VL - 26
SP - 69
EP - 82
JO - Spatial Statistics
JF - Spatial Statistics
ER -