Using INLA To Fit A Complex Point Process Model With Temporally Varying Effects – A Case Study

• Main Authors: Janine B. Illian, Sigrunn H. Sørbye, Ditte Hendrichsen
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Subjects: spatial point processes; spatial scale; replicated patterns; Greenland; Laplace; ovibos moschatus; Zackenberg
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.462.2386; http://research-repository.st-andrews.ac.uk/bitstream/10023/3306/1/JES_Illian_et_al.pdf

Integrated nested Laplace approximation (INLA) provides a fast and yet quite exact approach to fitting complex latent Gaussian models which comprise many statistical models in a Bayesian context, including log Gaussian Cox processes. This paper discusses how a joint log Gaussian Cox process model may be fitted to independent replicated point patterns. We illustrate the approach by fitting a model to data on the locations of muskoxen (Ovibos moschatus) herds in Zackenberg valley, Northeast Greenland and by detailing how this model is specified within the R-interface R-INLA. The paper strongly focuses on practical problems involved in the modelling process, including issues of spatial scale, edge effects and prior choices, and finishes with a discussion on models with varying boundary conditions.