  Prediction is a classic challenge in spatial statistics and the inclusion of
spatial covariates can greatly improve predictive performance when incorporated
into a model with latent spatial effects. It is desirable to develop flexible
regression models that allow for nonlinearities and interactions in the
covariate structure. Machine learning models have been suggested in the spatial
context, allowing for spatial dependence in the residuals, but fail to provide
reliable uncertainty estimates. In this paper, we investigate a novel
combination of a Gaussian process spatial model and a Bayesian Additive
Regression Tree (BART) model. The computational burden of the approach is
reduced by combining Markov chain Monte Carlo (MCMC) with the Integrated Nested
Laplace Approximation (INLA) technique. We study the performance of the method
via simulations and use the model to predict anthropometric responses,
collected via household cluster samples in Kenya.
