Title: Spatial Factor Models for High-Dimensional and Large Spatial Data: An Application in Forest Variable Mapping,
Abstract: Gathering information about forest variables is an expensive and arduous
activity. As such, directly collecting the data required to produce
high-resolution maps over large spatial domains is infeasible. Next generation
collection initiatives of remotely sensed Light Detection and Ranging (LiDAR)
data are specifically aimed at producing complete-coverage maps over large
spatial domains. Given that LiDAR data and forest characteristics are often
strongly correlated, it is possible to make use of the former to model,
predict, and map forest variables over regions of interest. This entails
dealing with the high-dimensional ($\sim$$10^2$) spatially dependent LiDAR
outcomes over a large number of locations (~10^5-10^6). With this in mind, we
develop the Spatial Factor Nearest Neighbor Gaussian Process (SF-NNGP) model,
and embed it in a two-stage approach that connects the spatial structure found
in LiDAR signals with forest variables. We provide a simulation experiment that
demonstrates inferential and predictive performance of the SF-NNGP, and use the
two-stage modeling strategy to generate complete-coverage maps of forest
variables with associated uncertainty over a large region of boreal forests in
interior Alaska.