Bayesian methods for ensembling (BPS)
Synopsis
Forecasts from different models can share information, disagree, and be wrong in different ways. A Bayesian analysis must describe how their information relates to the outcome being predicted. Bayesian predictive synthesis treats predictive distributions as information supplied by models or agents and uses a synthesis model to learn their biases and dependencies. Dynamic versions allow those relationships to change through time. The resulting framework supports univariate, multivariate, mixed-frequency, and spatial prediction, with the synthesis specified for the forecasting problem and evaluated using predictive performance. For causal inference, causal and regression synthesis combine heterogeneous treatment-effect estimates, propensity-score models, and outcome models to address uncertainty under model misspecification.
BPS tutorial
An introduction to Bayesian predictive synthesis, with a reading sequence, papers, and available code from the foundations through recent methods and applications.
Specific topics
- Predictive distributions
- Model and agent forecasts supply distributions that represent uncertainty about an outcome.
- Biases and dependencies
- A synthesis model learns how forecasts relate to the outcome and to one another.
- Dynamic synthesis
- Time-varying model parameters allow forecast biases and dependencies to change over time.
- Multivariate and mixed-frequency synthesis
- Joint outcomes and information observed at different frequencies require synthesis models that reflect their structure.
- Spatial synthesis
- Model parameters that vary by location allow the contribution of predictive information to change across space.
- Causal inference
- Causal synthesis combines heterogeneous treatment-effect estimates. Regression synthesis combines propensity-score and outcome models for doubly robust inference.
Selected papers
Multivariate Bayesian Predictive Synthesis in Macroeconomic Forecasting
Mixed-Frequency Bayesian Predictive Synthesis for Economic Nowcasting
Bayesian Spatial Predictive Synthesis
Predictive Synthesis under Sporadic Participation: Evidence from Inflation Density Surveys
Bayesian Causal Synthesis for Meta-Inference on Heterogeneous Treatment Effects
Ensemble Doubly Robust Bayesian Inference via Regression Synthesis
From Trial Averages to Target Effects: Bayesian CATE Synthesis with Randomized and Observational Evidence