Spatial data and Gaussian processes: A beautiful marriage

Alan Gelfand (Duke University, USA)

In the past twenty years analysis of spatial data has become increasingly model-based. Full specification of stochastic models for the spatial process being investigated enables full inference and uncertainty assessment regarding the process. Gaussian processes on subsets of R2 have become a fundamental specification for such modeling, particularly in settings where prediction is a primary goal. Therefore, focusing on the point-referenced case, we elaborate the substantial range of spatial settings where Gaussian processes have enabled rich and flexible modeling.
We start with the basic geostatistical model, in hierarchical form, moving to generalized spatial regression models, multivariate process models, and spatially varying coefficient models. We will consider the use of Gaussian processes to handle skewed distributions as well as nonparametric distributional models and also the role of Gaussian processes in dimension reduction strategies to accommodate large datasets. Also, we will look at less standard contexts including spatial extremes, spatial directional data, and spatial quantile regression. Modeling details, model fitting, and examples will be provided.