INLA or MCMC? A tutorial and comparative evaluation for spatial prediction in log-Gaussian Cox processes

Benjamin M. Taylor, Peter J. Diggle

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


We investigate two options for performing Bayesian inference on spatial log-Gaussian Cox processes assuming a spatially continuous latent field: Markov chain Monte Carlo (MCMC) and the integrated nested Laplace approximation (INLA). We first describe the device of approximating a spatially continuous Gaussian field by a Gaussian Markov random field on a discrete lattice, and present a simulation study showing that, with careful choice of parameter values, small neighbourhood sizes can give excellent approximations. We then introduce the spatial log-Gaussian Cox process and describe MCMC and INLA methods for spatial prediction within this model class. We report the results of a simulation study in which we compare the Metropolis-adjusted Langevin Algorithm (MALA) and the technique of approximating the continuous latent field by a discrete one, followed by approximate Bayesian inference via INLA over a selection of 18 simulated scenarios. The results question the notion that the latter technique is both significantly faster and more robust than MCMC in this setting; 100,000 iterations of the MALA algorithm running in 20 min on a desktop PC delivered greater predictive accuracy than the default INLA strategy, which ran in 4 min and gave comparative performance to the full Laplace approximation which ran in 39 min.

Original languageEnglish (US)
Pages (from-to)2266-2284
Number of pages19
JournalJournal of Statistical Computation and Simulation
Issue number10
StatePublished - 2014
Externally publishedYes


  • integrated nested Laplace approximation
  • log-Gaussian Cox process
  • Markov chain Monte Carlo
  • spatial modelling

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty


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