Visualisation for large-scale Gaussian updates

In geostatistics and also in other applications in science and engineering, it is now common to perform updates on Gaussian process models with many thousands or even millions of components. These large-scale inferences involve modelling, representational and computational challenges. We describe a visualization tool for large-scale Gaussian updates, the 'medal plot'. The medal plot shows the updated uncertainty at each observation location and also summarizes the sharing of information across observations, as a proxy for the sharing of information across the state vector (or latent process). As such, it reflects characteristics of both the observations and the statistical model.We illustrate with an application to assess mass trends in the Antarctic Ice Sheet, for which there are strong constraints from the observations and the physics.