Multi-Resolution Approximations of Gaussian Processes for Large Spatial Datasets
Abstract
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.
Citation
Gong, Wenlong (2018). Multi-Resolution Approximations of Gaussian Processes for Large Spatial Datasets. Doctoral dissertation, Texas A & M University. Available electronically from https : / /hdl .handle .net /1969 .1 /174463.