Hierarchical analysis of spatially autocorrelated ecological data using integrated nested Laplace approximation

Julien Beguin*, Sara Martino, Håvard Rue, Steven G. Cumming

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

57 Scopus citations


Spatial analysis of ecological data is central to many interesting questions in ecology. Bayesian implementation of spatially explicit models has received increasing attention from ecologists as Monte Carlo Markov Chain (MCMC) methods have become freely accessible. MCMC simulations offer a flexible framework for modelling extensive ecological data, but they also come with a wide range of problems regarding convergence, processing time and implementation. We introduce to ecologists an alternative procedure for fitting Bayesian hierarchical spatial models (BHSM) with quite general spatial covariance structures. This procedure uses integrated nested Laplace approximations (INLA) as an alternative to MCMC. We show, using a case study of species distribution model with binary areal data, that implementing BHSM with INLA does not require advanced programming skills, yields accurate results compared with MCMC and is rapid (e.g. a few seconds with small to moderate data sets). BHSMs efficiently removed spatial autocorrelation in the residuals and fairly evaluated uncertainty in parameter estimates and predictions. The rapidity of INLA significantly decreased the processing time and allowed both sensitivity analyses on priors and cross-validation tests to be performed within a reasonable amount of time, which ultimately increased model transparency.

Original languageEnglish (US)
Pages (from-to)921-929
Number of pages9
JournalMethods in Ecology and Evolution
Issue number5
StatePublished - Oct 2012
Externally publishedYes


  • Bayesian hierarchical spatial models
  • CAR model
  • MCMC
  • Matérn
  • Spatial autocorrelation
  • Species distribution model

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecological Modeling


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