TY - JOUR
T1 - Determinantal point process models on the sphere
AU - Møller, Jesper
AU - Nielsen, Morten
AU - Porcu, Emilio
AU - Rubak, Ege Holger
PY - 2018/5
Y1 - 2018/5
N2 - We consider determinantal point processes on the d-dimensional unit sphere S
d . These are finite point processes exhibiting repulsiveness and with moment properties determined by a certain determinant whose entries are specified by a so-called kernel which we assume is a complex covariance function defined on S
d ×S
d. We review the appealing properties of such processes, including their specific moment properties, density expressions and simulation procedures. Particularly, we characterize and construct isotropic DPPs models on S
d , where it becomes essential to specify the eigenvalues and eigenfunctions in a spectral representation for the kernel, and we figure out how repulsive isotropic DPPs can be. Moreover, we discuss the shortcomings of adapting existing models for isotropic covariance functions and consider strategies for developing new models, including a useful spectral approach.
AB - We consider determinantal point processes on the d-dimensional unit sphere S
d . These are finite point processes exhibiting repulsiveness and with moment properties determined by a certain determinant whose entries are specified by a so-called kernel which we assume is a complex covariance function defined on S
d ×S
d. We review the appealing properties of such processes, including their specific moment properties, density expressions and simulation procedures. Particularly, we characterize and construct isotropic DPPs models on S
d , where it becomes essential to specify the eigenvalues and eigenfunctions in a spectral representation for the kernel, and we figure out how repulsive isotropic DPPs can be. Moreover, we discuss the shortcomings of adapting existing models for isotropic covariance functions and consider strategies for developing new models, including a useful spectral approach.
KW - isotropic covariance function
KW - joint intensities
KW - quantifying repulsiveness
KW - Schoenberg representation
KW - spatial point process density
KW - spectral representation
KW - Isotropic covariance function
KW - Quantifying repulsiveness
KW - Spatial point process density
KW - Spectral representation
KW - Joint intensities
UR - http://www.scopus.com/inward/record.url?scp=85034844268&partnerID=8YFLogxK
U2 - 10.3150/16-BEJ896
DO - 10.3150/16-BEJ896
M3 - Journal article
SN - 1350-7265
VL - 24
SP - 1171
EP - 1201
JO - Bernoulli
JF - Bernoulli
IS - 2
ER -