Developing spatial modelling methodology for complex ecological data sets with INLA - the story of a symbiosis

Background/Question/Methods

In the spatial modelling literature, substantial advances have been made in the development of statistical methods for modelling spatial trend and correlation in the context  of  spatial point process models, in particular, Cox processes. Until very recently, fitting realistically complex models from this class was computationally prohibitive for any  but the smallest of datasets, largely preventing them from being used in practice. This is because fitting them involves time-consuming repeated solving of large, dense linear  systems of equations.

Results/Conclusions

However, the recent development of efficient and very accurate approximation methods for fitting models based on spatial random fields has made it possible to fit more  flexible and realistically complex spatial models without prohibitive computational cost (Rue et al. 2009; Lindgren et al. 2011, Illian et al. 2012a and b). These approaches  are based on integrated nested Laplace approximation (INLA), which, like Markov chain Monte Carlo (MCMC) methods, is a Bayesian estimation method, but is much faster (Rue et
al. 2009).  A key ingredient is the use of Markov random field models to replace the dense systems of equations with sparse alternatives. The R library R-INLA has been instrumental in making these methods available to non-specialist users.

This talk outlines the mutual benefits of developing both methodology and software as part of a continuing dialogue between method developers and ecologists. Highlights of this symbiosis and recent developments primarily resulting from it are presented.