Level set Cox processes

Hildeman, A., Bolin, D., Wallin, J. and Illian, J. B. (2018) Level set Cox processes. Spatial Statistics, 28, pp. 169-193. (doi:10.1016/j.spasta.2018.03.004)

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Abstract

An extension of the popular log-Gaussian Cox process (LGCP) model for spatial point patterns is proposed for 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 specified using a categorically valued random field. This classification is defined through level set operations on a Gaussian random field and allows for standard stationary covariance structures, such as the Matérn family, to be used to model 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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Illian, Professor Janine
Authors: Hildeman, A., Bolin, D., Wallin, J., and Illian, J. B.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Spatial Statistics
Publisher:Elsevier
ISSN:2211-6753
ISSN (Online):2211-6753
Published Online:04 April 2018
Copyright Holders:Copyright © 2018 Elsevier B.V.
First Published:First published in Spatial Statistics 28:169-193
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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