Our research program is focused on the statistical analysis of large spatial-temporal datasets, principally motivated by problems in the Earth sciences. For example, how do we best interpolate data from polar-orbiting satellites, which collect millions of observations per day but can only take measurements over one region at any given time? How should these interpolation procedures change based on the variable being measured and the location and time where an interpolation is required? How do we report accurate uncertainties, and how do we do all of this in a computationally efficient manner?
Much of our effort is devoted Gaussian process models, which are a powerful tool for analyzing spatial-temporal datasets but require careful input from the data analyst and impart a huge computational burden if used naively.
We have made advances in spectral methods, which leverage fast Fourier transform algorithms. In particular, we have developed periodic imputation methods that ameliorate edge effects and handle missing values naturally. We have two manuscripts on the topic, one for the parametric case, and one for the nonparametric case.
We have taken an interest in a Gaussian process approximation that was originally introduced by Aldo Vecchia in a 1988 paper. We showed how the approximation can be improved by reordering the observations and calculating it in chunks in this manuscript, where we also show that Vecchia's approximation is far more accurate than other state-of-the-art methods. We showed here that a generalization of Vecchia's approximation subsumes many popular existing approximations and introduced a novel sparse approximation. We evaluated the use of our generalized approximation in prediction tasks here
We also work on a number of other interesting problems, including data compression, climate change, medical imaging, and soil chemistry. Please see our full list of publications for more information.