| dc.description.abstract | Gaussian processes (GPs) are widely used in geospatial analysis, machine learning and many
application areas. We propose novel scalable methods to tackle two problems in Gaussian process modeling for large spatial datasets.
In the first study, we focus on the ubiquitous multi-scale phenomena in geophysical and other
applications. To model the multi-scale structure, we propose a novel multi-scale Vecchia (MSV)
approximation of GPs. In the MSV method, the increasingly small scales of spatial variation can
be captured by increasingly large sets of variables, and then an accurate approximation of the
spatial dependence is obtained from very large to very fine scales. By decomposing the observed dataset into different scales, our MSV method can visualize each scale and provide insights for the underlying processes. We develop an algorithm for automatically choosing the tuning parameters, and explore properties of the MSV approximation. We provide comparisons to existing approaches based on simulated data and using satellite measurements of land-surface temperature.
The second is concerned with global spatial processes. Rapid developments in satellite remote-sensing technology have enabled the collection of geospatial data on a global scale, and so there is an increased need for covariance functions that can capture spatial dependence on spherical domains. We propose a general method of constructing nonstationary, locally anisotropic covariance functions on the sphere based on covariance functions for Euclidean space. We provide theorems and conditions such that the resulting correlation function is isotropic or axially symmetric, for sensible parameterizations in specific applications. For modern large datasets on the sphere, the Vecchia approximation is applied to achieve computationally feasible inference. We provide illustrations and comparisons in numerical studies. | en |
