  Treeging combines the flexible mean structure of regression trees with the
covariance-based prediction strategy of kriging into the base learner of an
ensemble prediction algorithm. In so doing, it combines the strengths of the
two primary types of spatial and space-time prediction models: (1) models with
flexible mean structures (often machine learning algorithms) that assume
independently distributed data, and (2) kriging or Gaussian Process (GP)
prediction models with rich covariance structures but simple mean structures.
We investigate the predictive accuracy of treeging across a thorough and widely
varied battery of spatial and space-time simulation scenarios, comparing it to
ordinary kriging, random forest and ensembles of ordinary kriging base
learners. Treeging performs well across the board, whereas kriging suffers when
dependence is weak or in the presence of spurious covariates, and random forest
suffers when the covariates are less informative. Treeging also outperforms
these competitors in predicting atmospheric pollutants (ozone and PM$_{2.5}$)
in several case studies. We examine sensitivity to tuning parameters (number of
base learners and training data sampling proportion), finding they follow the
familiar intuition of their random forest counterparts. We include a discussion
of scaleability, noting that any covariance approximation techniques that
expedite kriging (GP) may be similarly applied to expedite treeging.
