Abstract
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 language | English (US) |
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Pages (from-to) | 2266-2284 |
Number of pages | 19 |
Journal | Journal of Statistical Computation and Simulation |
Volume | 84 |
Issue number | 10 |
DOIs | |
State | Published - 2014 |
Externally published | Yes |
Keywords
- 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