Multi-Resolution Approximations of Gaussian Processes for Large Spatial Datasets

Recent advances in remote-sensing techniques enabled accurate location geocoding and encouraged the collection of big spatial datasets over large domains. Data obtained in these settings are usually multivariate, with several spatial variables observed at each location. Statistical modeling for such spatial data is of ever-increasing importance in a variety of fields, including agriculture, climate science, astronomy, atmospheric science. Gaussian processes are popular and flexible models for such data, but they are computationally infeasible for large datasets. This dissertation is focused on spatial inference and prediction for big spatial data, and in particular on the computational feasibility of the statistical methodologies. It includes a general introduction to spatial statistics including Gaussian processes, spatial prediction as well as multivariate spatial data modeling. We also introduce Gaussian-process approximations that use basis functions at multiple resolutions to achieve fast inference and that can (approximately) represent any spatial covariance structure. Finally, we extend the multi-resolution approximation from univariate to multivariate spatial data, where the computation is even more expensive, by introducing latent dimensions into covariance modeling. The last part concludes the dissertation and discusses the future work