# Generalized Bayesian Additive Regression Trees Models: Beyond Conditional Conjugacy

arXiv: https://arxiv.org/abs/2202.09924 · HTML: https://mlsanity.com/paper/2202.09924/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 20 Feb 2022.

## Builds on (most cited first, 14 of 14)

- [Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition](https://mlsanity.com/paper/1707.02641/) (2017)
- [Discussion on "Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects" by Hahn, Murray and Carvalho](https://mlsanity.com/paper/2108.02836/) (2021)
- [Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects](https://mlsanity.com/paper/1706.09523/) (2017)
- [Bayesian Regression Tree Ensembles that Adapt to Smoothness and Sparsity](https://mlsanity.com/paper/1707.09461/) (2017)
- [Marginal likelihood computation for model selection and hypothesis testing: an extensive review](https://mlsanity.com/paper/2005.08334/) (2020)
- [bartMachine: Machine Learning with Bayesian Additive Regression Trees](https://mlsanity.com/paper/1312.2171/) (2013)
- [Stochastic tree ensembles for regularized nonlinear regression](https://mlsanity.com/paper/2002.03375/) (2020)
- [Individualized Treatment Effects with Censored Data via Fully Nonparametric Bayesian Accelerated Failure Time Models](https://mlsanity.com/paper/1706.06611/) (2017)
- [Semiparametric Mixed-Scale Models Using Shared Bayesian Forests](https://mlsanity.com/paper/1809.08521/) (2018)
- [Adaptive Conditional Distribution Estimation with Bayesian Decision Tree Ensembles](https://mlsanity.com/paper/2005.02490/) (2020)
- [Density Regression with Bayesian Additive Regression Trees](https://mlsanity.com/paper/2112.12259/) (2021)
- [XBART: Accelerated Bayesian Additive Regression Trees](https://mlsanity.com/paper/1810.02215/) (2018)
- [Bayesian quantile additive regression trees](https://mlsanity.com/paper/1607.02676/) (2016)
- [Fully Nonparametric Bayesian Additive Regression Trees](https://mlsanity.com/paper/1807.00068/) (2018)

## Built on by (most cited first, 8 of 8)

- [SoftBart: Soft Bayesian Additive Regression Trees](https://mlsanity.com/paper/2210.16375/) (2022)
- [Horseshoe Forests for High-Dimensional Causal Survival Analysis](https://mlsanity.com/paper/2507.22004/) (2025)
- [Generalized Bayesian Additive Regression Trees: Theory and Software](https://mlsanity.com/paper/2304.12505/) (2023)
- [Bayesian Additive Regression Networks](https://mlsanity.com/paper/2404.04425/) (2024)
- [BARMPy: Bayesian Additive Regression Models Python Package](https://mlsanity.com/paper/2404.04738/) (2024)
- [Heterogeneous Treatment Effect Estimation under Noncompliance in the Illinois Workplace Wellness Study with Bayesian Tree Ensembles](https://mlsanity.com/paper/2408.07765/) (2024)
- [Bayesian Neural Networks for Functional ANOVA model](https://mlsanity.com/paper/2510.00545/) (2025)
- [AI4BayesCode: From Natural Language Descriptions to Validated Modular Stateful Bayesian Samplers](https://mlsanity.com/paper/2605.18476/) (2026)

## Abstract (arXiv)

Bayesian additive regression trees have seen increased interest in recent years due to their ability to combine machine learning techniques with principled uncertainty quantification. The Bayesian backfitting algorithm used to fit BART models, however, limits their application to a small class of models for which conditional conjugacy exists. In this article, we greatly expand the domain of applicability of BART to arbitrary generalized BART models by introducing a very simple, tuning-parameter-free, reversible jump Markov chain Monte Carlo algorithm. Our algorithm requires only that the user be able to compute the likelihood and (optionally) its gradient and Fisher information. The potential applications are very broad; we consider examples in survival analysis, structured heteroskedastic regression, and gamma shape regression.