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.

翻译：预测是空间统计学中的经典挑战，当将空间协变量纳入具有潜在空间效应的模型时，能显著提升预测性能。发展允许协变量结构中存在非线性与交互作用的灵活回归模型具有重要价值。机器学习模型虽已被提出应用于空间场景（允许残差存在空间依赖性），但无法提供可靠的不确定性估计。本文研究了一种将高斯过程空间模型与贝叶斯加性回归树（BART）模型相结合的新型方法。通过将马尔可夫链蒙特卡洛（MCMC）与集成嵌套拉普拉斯近似（INLA）技术相结合，降低了该方法的计算负担。我们通过模拟实验评估了该方法的表现，并运用该模型对肯尼亚家庭聚类样本中收集的人体测量反应数据进行了预测。