# Bayesian Predictive Synthesis with Outcome-Dependent Pools

arXiv: https://arxiv.org/abs/1803.01984 · HTML: https://mlsanity.com/paper/1803.01984/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Mar 2018.

## Built on by (most cited first, 1 of 1)

- [When Do Language Models Add Value? Relative Competence in Hybrid Event Forecasting](https://mlsanity.com/paper/2609.12101/) (2026)

## Abstract (arXiv)

This paper reviews background and examples of Bayesian predictive synthesis (BPS), and develops details in a subset of BPS mixture models. BPS expands on standard Bayesian model uncertainty analysis for model mixing to provide a broader foundation for calibrating and combining predictive densities from multiple models or other sources. One main focus here is BPS as a framework for justifying and understanding generalized "linear opinion pools," where multiple predictive densities are combined with flexible mixing weights that depend on the forecast outcome itself, i.e., the setting of outcome-dependent model mixing. BPS also defines approaches to incorporating and exploiting dependencies across models defining forecasts, and to formally addressing the problem of model set incompleteness within the subjective Bayesian framework. In addition to an overview of general mixture-based BPS, new methodological developments for dynamic BPS -- involving calibration and pooling of sets of predictive distributions in a univariate time series setting -- are presented. These developments are exemplified in summaries of an analysis in a univariate financial time series study.