The integrated nested Laplace approximation applied to spatial log-Gaussian Cox process models.

Area of Science:

• Spatial Statistics
• Computational Ecology
• Geospatial Analysis

Background:

• Spatial point process models are valuable for mapping discrete events but computationally intensive.
• The log-Gaussian Cox process (LGCP) is a key model type, driven by a latent Gaussian field.
• Traditional fitting methods pose computational challenges for practical application.

Purpose of the Study:

• To demonstrate the practical application of Bayesian log-Gaussian Cox process (LGCP) models.
• To provide an accessible overview of Integrated Nested Laplace Approximation (INLA) for point process data.
• To facilitate the use of advanced spatial statistics methods by practitioners.

Main Methods:

• Utilized Integrated Nested Laplace Approximation (INLA) for efficient Bayesian inference.
• Employed a stochastic partial differential equations (SPDE) approach for sparse Gaussian field approximation.
• Applied pseudodata with a Poisson response for model extension and fitting.

Main Results:

• Demonstrated rapid computation for Bayesian LGCP models using INLA and SPDE.
• Successfully fitted models to both completely observed and incomplete spatial field datasets.
• Provided well-commented R code for reproducible analysis in the online supplement.

Conclusions:

• INLA with SPDE significantly reduces computational barriers for fitting LGCP models.
• These methods are now accessible to spatial statistics practitioners without extensive point process theory knowledge.
• The approach enables effective mapping of discrete spatial events using readily available data.