# Predictive Density Combination Using a Tree-Based Synthesis Function

arXiv: https://arxiv.org/abs/2311.12671 · HTML: https://mlsanity.com/paper/2311.12671/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 54 references that are in the map.
- First posted on arXiv 21 Nov 2023.

## Builds on (most cited first, 8 of 8)

- [Nowcasting in a Pandemic using Non-Parametric Mixed Frequency VARs](https://mlsanity.com/paper/2008.12706/) (2020)
- [Ancillarity-Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Estimation of Stochastic Volatility Models](https://mlsanity.com/paper/1706.05280/) (2017)
- [Dynamic Bayesian Predictive Synthesis in Time Series Forecasting](https://mlsanity.com/paper/1601.07463/) (2016)
- [Bayesian Nonparametric Calibration and Combination of Predictive Distributions](https://mlsanity.com/paper/1502.07246/) (2015)
- [Inference in Bayesian Additive Vector Autoregressive Tree Models](https://mlsanity.com/paper/2006.16333/) (2020)
- [Multivariate Bayesian Predictive Synthesis in Macroeconomic Forecasting](https://mlsanity.com/paper/1711.01667/) (2017)
- [Bayesian Predictive Decision Synthesis](https://mlsanity.com/paper/2206.03815/) (2022)
- [Local Prediction Pools](https://mlsanity.com/paper/2112.09073/) (2021)

## Abstract (arXiv)

Bayesian predictive synthesis (BPS) provides a method for combining multiple predictive distributions based on agent/expert opinion analysis theory and encompasses a range of existing density forecast pooling methods. The key ingredient in BPS is a ``synthesis'' function. This is typically specified parametrically as a dynamic linear regression. In this paper, we develop a nonparametric treatment of the synthesis function using regression trees. We show the advantages of our tree-based approach in two macroeconomic forecasting applications. The first uses density forecasts for GDP growth from the euro area's Survey of Professional Forecasters. The second combines density forecasts of US inflation produced by many regression models involving different predictors. Both applications demonstrate the benefits -- in terms of improved forecast accuracy and interpretability -- of modeling the synthesis function nonparametrically.