  In areal unit data with missing or suppressed data, it desirable to create
models that are able to predict observations that are not available.
Traditional statistical methods achieve this through Bayesian hierarchical
models that can capture the unexplained residual spatial autocorrelation
through conditional autoregressive (CAR) priors, such that they can make
predictions at geographically related spatial locations. In contrast, typical
machine learning approaches such as random forests ignore this residual
autocorrelation, and instead base predictions on complex non-linear
feature-target relationships. In this paper, we propose CAR-Forest, a novel
spatial prediction algorithm that combines the best features of both approaches
by fusing them together. By iteratively refitting a random forest combined with
a Bayesian CAR model in one algorithm, CAR-Forest can incorporate flexible
feature-target relationships while still accounting for the residual spatial
autocorrelation. Our results, based on a Scottish housing price data set, show
that CAR-Forest outperforms Bayesian CAR models, random forests, and the
state-of-the-art hybrid approach, geographically weighted random forest,
providing a state-of-the-art framework for small-area spatial prediction.
