From Sea Level Rise to COVID-19: Extending a Bayesian Hierarchical Model to unfamiliar problems with the 4D-Modeller framework

The recently completed European Research Council project “Global Mass” (www.globalmass.eu) aimed to reconcile the global sea-level budget as measured through a variety of satellite and in-situ data sources using a space-time Bayesian Hierarchical Model (BHM). The BHM uses Gaussian latent processes to estimate the contribution and uncertainty of different physical processes such as land hydrology, ocean thermal expansion, and glacier melt, to ongoing sea-level rise. Each process has a unique spatial and temporal length scale, which can be provided as a prior or inferred from the observations within the model. The BHM can separate the physical process sources represented in the data, model the stationarity of these processes, and estimate their uncertainty globally. A particular strength of the BHM is its ability to estimate and separate the different processes, from data with disparate spatial and temporal sampling and for observations that are influenced by multiple processes. This is often termed the source separation problem and we utilize novel statistical methods to solve for this and for dimensional reduction to allow the problem to be computationally tractable. We use the Integrated Nested Laplace Approximation (INLA) framework to approximate the observation layer and for the inference itself due to its accuracy and computational speed. The BHM has the potential to address a wider class of spatio-temporal inference problems and here we introduce the model structure (named 4D-modeller) and apply it to new classes of problem to extend its versatility. We apply it to COVID-19 transmittability in England and hydrology uncertainties related to hydropower reservoirs in Norway: problems that span social and physical sciences.