A toolbox for fitting complex spatial point process models using integrated nested Laplace approximation (INLA) This paper develops a methodology that provides a toolbox for routinely fitting complex models to realistic spatial point pattern data. We consider models that are based on log-Gaussian Cox processes and include local interaction in these by considering constructed covariates. This enables us to use integrated nested Laplace approximation and to considerably speed up the inferential task. In addition, methods for model comparison and model assessment facilitate the modelling process. The performance of the approach is assessed in a simulation study. To demonstrate the versatility of the approach, models are fitted to two rather different examples, a large rainforest data set with covariates and a point pattern with multiple marks.

References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Micheas, Athanasios C.; Chen, Jiaxun: sppmix: Poisson point process modeling using normal mixture models (2018)
  2. Illian, Janine B.; Burslem, David F. R. P.: Improving the usability of spatial point process methodology: an interdisciplinary dialogue between statistics and ecology (2017)
  3. Shaddick, Gavin; Zidek, James V.: Spatio-temporal methods in environmental epidemiology (2016)
  4. Benjamin M. Taylor, Tilman M. Davies, Barry S. Rowlingson, Peter J. Diggle: Bayesian Inference and Data Augmentation Schemes for Spatial, Spatiotemporal and Multivariate Log-Gaussian Cox Processes in R (2015) not zbMATH
  5. Blangiardo, Marta; Cameletti, Michela: Spatial and spatio-temporal Bayesian models with R-INLA (2015)
  6. Ferkingstad, Egil; Rue, Håvard: Improving the INLA approach for approximate Bayesian inference for latent Gaussian models (2015)
  7. Francesco Finazzi; Alessandro Fassò: D-STEM: A Software for the Analysis and Mapping of Environmental Space-Time Variables (2014) not zbMATH
  8. Rajala, T.; Penttinen, A.: Bayesian analysis of a Gibbs hard-core point pattern model with varying repulsion range (2014)
  9. Martins, Thiago G.; Simpson, Daniel; Lindgren, Finn; Rue, Håvard: Bayesian computing with INLA: new features (2013)
  10. Gneiting, Tilmann (ed.): Section on the special year for mathematics of planet Earth (MPE 2013) (2012)
  11. Illian, Janine B.; Sørbye, Sigrunn H.; Rue, Håvard: A toolbox for fitting complex spatial point process models using integrated nested Laplace approximation (INLA) (2012)
  12. King, Ruth; Illian, Janine B.; King, Stuart E.; Nightingale, Glenna F.; Hendrichsen, Ditte K.: A Bayesian approach to fitting Gibbs processes with temporal random effects (2012)
  13. Schrödle, Birgit; Held, Leonhard: A primer on disease mapping and ecological regression using (\mathttINLA) (2011)