Research

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.

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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

Research