Combining Large Numbers of Density Predictions with Bayesian Predictive Synthesis

Bayesian predictive synthesis is a flexible method of combining density predictions. The flexibility comes from the ability to choose an arbitrary synthesis function to combine predictions. I study the choice of synthesis function when combining large numbers of predictions—a common occurrence in macroeconomics. Estimating combination weights with many predictions is difficult, so I consider shrinkage priors and factor modelling techniques to address this problem. The dense weights of factor modelling provide an interesting contrast with the sparse weights implied by shrinkage priors. I find that the sparse weights of shrinkage priors perform well across exercises.