Bayesian Additive Regression Trees for Varying Coefficient Models
A linear varying coefficient model (VCM) posits a linear relationship between an outcome and several covariates but allows that relationship to change as a function of additional effect modifiers. Despite a long history of study and use in statistics and econometrics, most methods for fitting VCMs cannot accommodate multivariate effect modifiers without imposing restrictive functional form assumptions or involving computationally intensive hyperparameter tuning.
In this talk, I will introduce VCBART, which flexibly estimates covariate effects in a VCM using regression tree ensembles. With simple default settings, VCBART achieves state-of-the-art effect estimation and uncertainty quantification and achieves near-minimax-optimal posterior contraction rates. I will then describe recent extensions to VCBART that leverage global-local shrinkage priors that enable users to fit sparse, high-dimensional VCMs with multiple, possibly dependent, outcomes. These extensions also display excellent empirical performance and desirable theoretical properties.
The talk is based work described in three manuscripts:
https://arxiv.org/abs/2510.08204
