Bayesian Predictive Synthesis with Outcome-Dependent Pools

TL;DR

This paper advances Bayesian predictive synthesis by developing outcome-dependent model pooling, incorporating dependencies among models, and applying dynamic calibration methods, with a focus on financial time series analysis.

Contribution

It introduces new methodological frameworks for outcome-dependent model mixing and dynamic BPS, expanding the applicability of Bayesian predictive synthesis.

Findings

Demonstrates outcome-dependent pooling improves predictive accuracy.

Develops methods for incorporating model dependencies.

Applies techniques to financial time series data.

Abstract

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.