Predictive Density Combination Using Bayesian Machine Learning

Abstract: Based on agent opinion analysis theory, Bayesian predictive synthesis (BPS) is a framework for combining predictive distributions in the face of model uncertainty. In this article, we generalize existing parametric implementations of BPS by showing how to combine competing probabilistic forecasts using interpretable Bayesian tree-based machine learning methods. We demonstrate the advantages of our approach—in terms of improved forecast accuracy and interpretability—via two macroeconomic forecasting applications. The first uses density forecasts for GDP growth from the euro area's Survey of Professional Forecasters. The second combines density forecasts of U.S. inflation produced by many simple regression models.