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Level set Cox processes

Wallin, Jonas LU ; Bolin, David ; Hildeman, Anders and Illian, Janine (2018) In Spatial Statistics 28. p.169-193
Abstract
The log-Gaussian Cox process (LGCP) is a popular point process for modeling noninteracting spatial point patterns. This paper extends the LGCP model to handle data exhibiting fundamentally different behaviors in different subregions of the spatial domain. The aim of the analyst might be either to identify and classify these regions, to perform kriging, or to derive some properties of the parameters driving the random field in one or several of the subregions. The extension is based on replacing the latent Gaussian random field in the LGCP by a latent spatial mixture model. The mixture model is specified using a latent, categorically valued, random field induced by level set operations on a Gaussian random field. Conditional on the... (More)
The log-Gaussian Cox process (LGCP) is a popular point process for modeling noninteracting spatial point patterns. This paper extends the LGCP model to handle data exhibiting fundamentally different behaviors in different subregions of the spatial domain. The aim of the analyst might be either to identify and classify these regions, to perform kriging, or to derive some properties of the parameters driving the random field in one or several of the subregions. The extension is based on replacing the latent Gaussian random field in the LGCP by a latent spatial mixture model. The mixture model is specified using a latent, categorically valued, random field induced by level set operations on a Gaussian random field. Conditional on the classification, the intensity surface for each class is modeled by a set of independent Gaussian random fields. This allows for standard stationary covariance structures, such as the Matérn family, to be used to model Gaussian random fields with some degree of general smoothness but also occasional and structured sharp discontinuities. A computationally efficient MCMC method is proposed for Bayesian inference and we show consistency of finite dimensional approximations of the model. Finally, the model is fitted to point pattern data derived from a tropical rainforest on Barro Colorado island, Panama. We show that the proposed model is able to capture behavior for which inference based on the standard LGCP is biased. (Less)
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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Spatial Statistics
volume
28
pages
169 - 193
publisher
Elsevier
external identifiers
  • scopus:85045031909
ISSN
2211-6753
DOI
10.1016/j.spasta.2018.03.004
language
English
LU publication?
yes
id
724705e9-3269-4ef4-a29b-3d012cefd718
alternative location
https://arxiv.org/pdf/1708.06982.pdf
date added to LUP
2017-12-20 09:01:35
date last changed
2021-09-22 01:20:06
@article{724705e9-3269-4ef4-a29b-3d012cefd718,
  abstract     = {The log-Gaussian Cox process (LGCP) is a popular point process for modeling noninteracting spatial point patterns. This paper extends the LGCP model to handle data exhibiting fundamentally different behaviors in different subregions of the spatial domain. The aim of the analyst might be either to identify and classify these regions, to perform kriging, or to derive some properties of the parameters driving the random field in one or several of the subregions. The extension is based on replacing the latent Gaussian random field in the LGCP by a latent spatial mixture model. The mixture model is specified using a latent, categorically valued, random field induced by level set operations on a Gaussian random field. Conditional on the classification, the intensity surface for each class is modeled by a set of independent Gaussian random fields. This allows for standard stationary covariance structures, such as the Matérn family, to be used to model Gaussian random fields with some degree of general smoothness but also occasional and structured sharp discontinuities. A computationally efficient MCMC method is proposed for Bayesian inference and we show consistency of finite dimensional approximations of the model. Finally, the model is fitted to point pattern data derived from a tropical rainforest on Barro Colorado island, Panama. We show that the proposed model is able to capture behavior for which inference based on the standard LGCP is biased.},
  author       = {Wallin, Jonas and Bolin, David and Hildeman, Anders and Illian, Janine},
  issn         = {2211-6753},
  language     = {eng},
  pages        = {169--193},
  publisher    = {Elsevier},
  series       = {Spatial Statistics},
  title        = {Level set Cox processes},
  url          = {http://dx.doi.org/10.1016/j.spasta.2018.03.004},
  doi          = {10.1016/j.spasta.2018.03.004},
  volume       = {28},
  year         = {2018},
}