Evaluating a Bayesian modelling approach (INLA-SPDE) for environmental mapping.

Understanding the uncertainty in spatial modelling of environmental variables is important because it provides the end-users with the reliability of the maps. Over the past decades, Bayesian statistics has been successfully used. However, the conventional simulation-based Markov Chain Monte Carlo (MCMC) approaches are often computationally intensive. In this study, the performance of a novel Bayesian inference approach called Integrated Nested Laplace Approximation with Stochastic Partial Differential Equation (INLA-SPDE) was evaluated using independent calibration and validation datasets of various skewed and non-skewed soil properties and was compared with a linear mixed model estimated by residual maximum likelihood (REML-LMM). It was found that INLA-SPDE was equivalent to REML-LMM in terms of the model performance and was similarly robust with sparse datasets (i.e. 40-60 samples). In comparison, INLA-SPDE was able to estimate the posterior marginal distributions of the model parameters without extensive simulations. It was concluded that INLA-SPDE had the potential to map the spatial distribution of environmental variables along with their posterior marginal distributions for environmental management. Some drawbacks were identified with INLA-SPDE, including artefacts of model response due to the use of triangle meshes and a longer computational time when dealing with non-Gaussian likelihood families.