  High resolution geospatial data are challenging because standard
geostatistical models based on Gaussian processes are known to not scale to
large data sizes. While progress has been made towards methods that can be
computed more efficiently, considerably less attention has been devoted to big
data methods that allow the description of complex relationships between
several outcomes recorded at high resolutions by different sensors. Our
Bayesian multivariate regression models based on spatial multivariate trees
(SpamTrees) achieve scalability via conditional independence assumptions on
latent random effects following a treed directed acyclic graph.
Information-theoretic arguments and considerations on computational efficiency
guide the construction of the tree and the related efficient sampling
algorithms in imbalanced multivariate settings. In addition to simulated data
examples, we illustrate SpamTrees using a large climate data set which combines
satellite data with land-based station data. Source code is available at
https://github.com/mkln/spamtree
