Level set Cox processes
Anders Hildeman, David Bolin, Jonas Wallin, Janine B. Illian

TL;DR
This paper extends the log-Gaussian Cox process model by incorporating a spatial mixture model with level set operations, enabling better modeling of heterogeneous spatial point patterns with sharp discontinuities.
Contribution
The paper introduces a novel extension of LGCP using a latent spatial mixture model with level set operations, allowing for modeling non-stationary and discontinuous spatial processes.
Findings
The new model captures heterogeneous spatial behaviors more accurately.
Bayesian inference via an efficient MCMC method is developed.
Application to rainforest data demonstrates improved fit over standard LGCP.
Abstract
The log-Gaussian Cox process (LGCP) is a popular point process for modeling non-interacting 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…
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Taxonomy
TopicsStatistical Methods and Inference · Bayesian Methods and Mixture Models · Advanced Statistical Process Monitoring
