Computation and Visualisation for large-scale Gaussian updates

TL;DR

This paper introduces a diagnostic and visualization tool called the 'medal plot' for large-scale Gaussian process updates, addressing computational and representational challenges in geostatistics and related fields.

Contribution

It presents the medal plot as a novel diagnostic tool for visualizing uncertainty and information sharing in large-scale Gaussian updates, with applications in geostatistics.

Findings

The medal plot effectively visualizes uncertainty for each observation.

It helps identify unexpected features in large-scale Gaussian models.

Application to Antarctic Ice Sheet mass trends demonstrates practical utility.

Abstract

In geostatistics, and also in other applications in science and engineering, we are now performing updates on Gaussian process models with many thousands or even millions of components. These large-scale inferences involve computational challenges, because the updating equations cannot be solved as written, owing to the size and cost of the matrix operations. They also involve representational challenges, to account for judgements of heterogeneity concerning the underlying fields, and diverse sources of observations. Diagnostics are particularly valuable in this situation. We present a diagnostic and visualisation tool for large-scale Gaussian updates, the `medal plot'. This shows the updated uncertainty for each observation, and also summarises the sharing of information across observations, as a proxy for the sharing of information across the state vector. It allows us to `sanity-check' the code implementing the update, but it can also reveal unexpected features in our modelling. We discuss computational issues for large-scale updates, and we illustrate with an application to assess mass trends in the Antarctic Ice Sheet.