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).
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.
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.