Gaussian Process Regression and Bayesian Model Averaging: An Alternative Approach to Modeling Spatial Phenomena

Gaussian Process Regression (GPR) is a nonparametric technique that is capable of yielding reliable out‐of‐sample predictions in the presence of highly nonlinear unknown relationships between dependent and explanatory variables. But in terms of identifying relevant explanatory variables, this method is far less explicit about questions of statistical significance. In contrast, more traditional spatial econometric models, such as spatial autoregressive models or spatial error models, place rather strong prior restrictions on the functional form of relationships, but allow direct inference with respect to explanatory variables. In this article, we attempt to combine the best of both techniques by augmenting GPR with a Bayesian Model Averaging (BMA) component that allows for the identification of statistically relevant explanatory variables while retaining the predictive performance of GPR. In particular, GPR‐BMA yields a posterior probability interpretation of model‐inclusion frequencies that provides a natural measure of the statistical relevance of each variable. Moreover, while such frequencies offer no direct information about the signs of local marginal effects, it is shown that partial derivatives based on the mean GPR predictions do provide such information. We illustrate the additional insights made possible by this approach by applying GPR‐BMA to a benchmark BMA data set involving potential determinants of cross‐country economic growth. It is shown that localized marginal effects based on partial derivatives of mean GPR predictions yield additional insights into comparative growth effects across countries.