TY - JOUR
T1 - Second-order semi-parametric inference for multivariate log Gaussian Cox processes
AU - Hessellund, Kristian Bjørn
AU - Xu, Ganggang
AU - Guan, Yongtao
AU - Waagepetersen, Rasmus
N1 - Publisher Copyright:
© 2021 John Wiley & Sons Ltd
PY - 2022/1
Y1 - 2022/1
N2 - This paper introduces a new approach to inferring the second-order properties of a multivariate log Gaussian Cox process (LGCP) with a complex intensity function. We assume a semi-parametric model for the multivariate intensity function containing an unspecified complex factor common to all types of points. Given this model, we construct a second-order conditional composite likelihood to infer the pair correlation and cross pair correlation functions of the LGCP. Crucially this likelihood does not depend on the unspecified part of the intensity function. We also introduce a cross-validation method for model selection and an algorithm for regularized inference that can be used to obtain sparse models for cross pair correlation functions. The methodology is applied to simulated data as well as data examples from microscopy and criminology. This shows how the new approach outperforms existing alternatives where the intensity functions are estimated non-parametrically.
AB - This paper introduces a new approach to inferring the second-order properties of a multivariate log Gaussian Cox process (LGCP) with a complex intensity function. We assume a semi-parametric model for the multivariate intensity function containing an unspecified complex factor common to all types of points. Given this model, we construct a second-order conditional composite likelihood to infer the pair correlation and cross pair correlation functions of the LGCP. Crucially this likelihood does not depend on the unspecified part of the intensity function. We also introduce a cross-validation method for model selection and an algorithm for regularized inference that can be used to obtain sparse models for cross pair correlation functions. The methodology is applied to simulated data as well as data examples from microscopy and criminology. This shows how the new approach outperforms existing alternatives where the intensity functions are estimated non-parametrically.
UR - http://www.scopus.com/inward/record.url?scp=85119499394&partnerID=8YFLogxK
U2 - 10.1111/rssc.12530
DO - 10.1111/rssc.12530
M3 - Journal article
AN - SCOPUS:85119499394
SN - 0035-9254
VL - 71
SP - 244
EP - 268
JO - Journal of the Royal Statistical Society. Series C: Applied Statistics
JF - Journal of the Royal Statistical Society. Series C: Applied Statistics
IS - 1
ER -