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 journalArticle

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 languageEnglish (US)
Pages (from-to)2266-2284
Number of pages19
JournalJournal of Statistical Computation and Simulation
Volume84
Issue number10
DOIs
StatePublished - 2014
Externally publishedYes

Fingerprint

Cox Process
Spatial Prediction
Laplace Approximation
Markov Chain Monte Carlo
Gaussian Process
Markov processes
Evaluation
Approximate Bayesian Inference
Simulation Study
Gaussian Markov Random Field
Laplace's Method
Gaussian Fields
Bayesian inference
Approximation Methods
Cox process
Markov chain Monte Carlo
Prediction
Integrated nested Laplace approximation
Iteration
Scenarios

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

Cite this

INLA or MCMC? A tutorial and comparative evaluation for spatial prediction in log-Gaussian Cox processes. / Taylor, Benjamin M.; Diggle, Peter J.

In: Journal of Statistical Computation and Simulation, Vol. 84, No. 10, 2014, p. 2266-2284.

Research output: Contribution to journalArticle

@article{4cafe92466a64d5bb08ed628541c04c8,
title = "INLA or MCMC? A tutorial and comparative evaluation for spatial prediction in log-Gaussian Cox processes",
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.",
keywords = "integrated nested Laplace approximation, log-Gaussian Cox process, Markov chain Monte Carlo, spatial modelling",
author = "Taylor, {Benjamin M.} and Diggle, {Peter J.}",
year = "2014",
doi = "10.1080/00949655.2013.788653",
language = "English (US)",
volume = "84",
pages = "2266--2284",
journal = "Journal of Statistical Computation and Simulation",
issn = "0094-9655",
publisher = "Taylor and Francis Ltd.",
number = "10",

}

TY - JOUR

T1 - INLA or MCMC? A tutorial and comparative evaluation for spatial prediction in log-Gaussian Cox processes

AU - Taylor, Benjamin M.

AU - Diggle, Peter J.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - integrated nested Laplace approximation

KW - log-Gaussian Cox process

KW - Markov chain Monte Carlo

KW - spatial modelling

UR - http://www.scopus.com/inward/record.url?scp=84902670046&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902670046&partnerID=8YFLogxK

U2 - 10.1080/00949655.2013.788653

DO - 10.1080/00949655.2013.788653

M3 - Article

VL - 84

SP - 2266

EP - 2284

JO - Journal of Statistical Computation and Simulation

JF - Journal of Statistical Computation and Simulation

SN - 0094-9655

IS - 10

ER -