Uncertainty Quantification and Experimental Design for Large-Scale Linear Inverse Problems under Gaussian Process Priors

This work extends traditional sequential uncertainty reduction strategies (SUR) to large-scale Bayesian inverse problems. By introducing a new, implicit representation of the posterior covariance matrix of a Gaussian process, we are able to scale SUR real-world 3D problems. The introduced techniques are demonstrated on a set estimation problems in gravimetric inversion (Stromboli volcano).

published version at SIAM JUQ

arXiv version

Disintegration of Gaussian Measures for Sequential Assimilation of Linear Operator Data

In this article, we provide a theoretical framework for conditioning Gaussian processes (GP) under linear operator data by leveraging the theory of Gaussian measures. Disintegrations of Gaussian measures offer a sound theoretical framework for conditioning under linear operator data, and we extend previous results to allow conditioning non-centered measures. To ensure that the measure results transfer to the GP world, we provide conditions for ensuring that a GP with trajectories in a given Banach space induces a measure on that space.

arXiv version

Learning excursion sets of vector-valued Gaussian random fields for autonomous ocean sampling

In this work, we extend SUR strategies to multivariate settings. In passing, we provide a new way of looking at the GP co-kriging equations that makes them form-invariant across all dimensions of the output and allows computing semi-analytical formulae for the SUR criterion. The techniques are demonstrated on a river plume estimation problem.

arXiv version

published version at Annals of Applied Statistics