Visualization for Large-scale Gaussian Updates
TL;DR: A visualization tool for large‐scale Gaussian updates, the ‘medal plot’, is described, which reflects characteristics of both the observations and the statistical model and is illustrated with an application to assess mass trends in the Antarctic Ice Sheet.
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Abstract: In geostatistics (and also in other applications in science and engineering) we are now performing updates on Gaussian process models with thousands 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 initial and 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 West Antarctic Ice Sheet.
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Figures
Figure 1: Toy problem showing medals for various configurations of the prior variance and observation error variance, and the proximity of other observations. The prior process is stationary with standard deviation 2 and correlation length 30. See Section 3.2 for details. 
Figure 2: Medal plot for GRACE footprints over Antarctica, with distances in kilometres. The solid line is the grounding line (where the ice begins to float), and the dashed line is the coastline (which includes the floating ice). See Section 4 for details of the application and observations. We have used a semi-transparent blue instead of white for the annulus.
Citations
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•Posted Content
Computation and Visualisation for large-scale Gaussian updates
TL;DR: This work presents a diagnostic and visualisation tool for large-scale Gaussian updates, the `medal plot', which shows the updated uncertainty for each observation, and also summarises the sharing of information across observations, as a proxy for the shared information across the state vector.
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Bayesian Statistical Inference for Psychological Research
Jie W Weiss,David J. Weiss +1 more
- 10 Oct 2008
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