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

Area of Science:

• Environmental Science
• Geostatistics
• Computational Statistics

Background:

• Spatial modeling of environmental variables is crucial for map reliability.
• Bayesian statistics are widely used but often computationally intensive via Markov Chain Monte Carlo (MCMC).

Purpose of the Study:

• To evaluate the performance of Integrated Nested Laplace Approximation with Stochastic Partial Differential Equation (INLA-SPDE) for spatial modeling.
• To compare INLA-SPDE with a conventional linear mixed model (REML-LMM).

Main Methods:

• INLA-SPDE was tested using calibration and validation datasets for soil properties.
• Performance was assessed against a residual maximum likelihood linear mixed model (REML-LMM).

Main Results:

• INLA-SPDE demonstrated performance equivalent to REML-LMM, even with sparse data.
• INLA-SPDE estimated posterior marginal distributions without extensive simulations.
• Drawbacks included mesh artefacts and longer computation for non-Gaussian data.

Conclusions:

• INLA-SPDE is a viable alternative for spatial mapping of environmental variables, offering uncertainty quantification.
• The method has potential for environmental management applications.
• Further refinement is needed to address computational limitations with specific data types.