# VCBART: Bayesian trees for varying coefficients

arXiv: https://arxiv.org/abs/2003.06416 · HTML: https://mlsanity.com/paper/2003.06416/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2020.

## Built on by (most cited first, 7 of 7)

- [Accounting for shared covariates in semi-parametric Bayesian additive regression trees](https://mlsanity.com/paper/2108.07636/) (2021)
- [Hierarchical Embedded Bayesian Additive Regression Trees](https://mlsanity.com/paper/2204.07207/) (2022)
- [SoftBart: Soft Bayesian Additive Regression Trees](https://mlsanity.com/paper/2210.16375/) (2022)
- [The Bayesian Context Trees State Space Model for time series modelling and forecasting](https://mlsanity.com/paper/2308.00913/) (2023)
- [Bayesian Data Sketching for Varying Coefficient Regression Models](https://mlsanity.com/paper/2506.00270/) (2025)
- [Heterogeneous Distributed Lag Models to Estimate Personalized Effects of Maternal Exposures to Air Pollution](https://mlsanity.com/paper/2109.13763/) (2021)
- [Heterogeneous Treatment Effect Estimation under Noncompliance in the Illinois Workplace Wellness Study with Bayesian Tree Ensembles](https://mlsanity.com/paper/2408.07765/) (2024)

## Abstract (arXiv)

The linear varying coefficient models posits a linear relationship between an outcome and covariates in which the covariate effects are modeled as functions of additional effect modifiers. Despite a long history of study and use in statistics and econometrics, state-of-the-art varying coefficient modeling methods cannot accommodate multivariate effect modifiers without imposing restrictive functional form assumptions or involving computationally intensive hyperparameter tuning. In response, we introduce VCBART, which flexibly estimates the covariate effect in a varying coefficient model using Bayesian Additive Regression Trees. With simple default settings, VCBART outperforms existing varying coefficient methods in terms of covariate effect estimation, uncertainty quantification, and outcome prediction. We illustrate the utility of VCBART with two case studies: one examining how the association between later-life cognition and measures of socioeconomic position vary with respect to age and socio-demographics and another estimating how temporal trends in urban crime vary at the neighborhood level. An R package implementing VCBART is available at https://github.com/skdeshpande91/VCBART