Bayesian hierarchical stacking: Some models are (somewhere) useful

Understand

Stacking is a widely used model averaging technique that asymptotically yields optimal predictions among linear averages.

• We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can further improve the stacked mixture with a hierarchical model.
• We generalize stacking to Bayesian hierarchical stacking.
• The model weights are varying as a function of data, partially-pooled, and inferred using Bayesian inference.