Overcoming challenges in spatio-temporal modelling of large-scale (global) data

Modelling spatio-temporal data on a large scale presents a number of obstacles for statisticians and environmental scientists. Issues such as computational complexity, combining point and areal data, separation of sources into their component processes, and the handling of both large volumes of data in some areas and sparse data in others must be considered. We discuss methods to overcome such challenges within a Bayesian hierarchical modelling framework using INLA.

In particular, we illustrate the approach using the example of source-separation of geophysical signals both on a continental and global scale. In such a setting, data tends to be available both at a local and areal level. We propose a novel approach for integrating such sources together using the INLA-SPDE method, which is normally reserved for point-level data. Additionally, the geophysical processes involved are both spatial (time-invariant) and spatio-temporal in nature. Separation of such processes into physically sensible components requires careful modelling and consideration of priors (such as physical model outputs where data is sparse), which will be discussed. We also consider methods to overcome the computational costs of modelling on such a large scale, from efficient mesh design, to thinning/aggregating of data, to considering alternative approaches for inference. This holistic approach to modelling of large-scale data ensures that spatial and spatio-temporal processes can be sensibly separated into their component parts, without being prohibitively expensive to model.