  Bayesian predictive synthesis (BPS) provides a method for combining multiple
predictive distributions based on agent/expert opinion analysis theory and
encompasses a range of existing density forecast pooling methods. The key
ingredient in BPS is a ``synthesis'' function. This is typically specified
parametrically as a dynamic linear regression. In this paper, we develop a
nonparametric treatment of the synthesis function using regression trees. We
show the advantages of our tree-based approach in 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 US inflation produced by many regression models involving
different predictors. Both applications demonstrate the benefits -- in terms of
improved forecast accuracy and interpretability -- of modeling the synthesis
function nonparametrically.
