2014/06/19 by Jonathan Rougier, J Rougier, Rougier, Jonathan +5
Computer Science · Environmental Science · Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Hydrology and Watershed Management Studies #Soil Geostatistics and Mapping #stat.CO
paper · pdf · doi:10.48550/arxiv.1406.5005
arxiv created 2014/06/19 · openalex publication_date 2014/06/19 · arxiv updated 2014/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.