# Discussion on "Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects" by Hahn, Murray and Carvalho

arXiv: https://arxiv.org/abs/2108.02836 · HTML: https://mlsanity.com/paper/2108.02836/

## Key facts

- Cited by 77 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2021.

## Built on by (most cited first, 30 of 77)

- [CausalPFN: Amortized Causal Effect Estimation via In-Context Learning](https://mlsanity.com/paper/2506.07918/) (2025)
- [In Search of Insights, Not Magic Bullets: Towards Demystification of the Model Selection Dilemma in Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2302.02923/) (2023)
- [SurvITE: Learning Heterogeneous Treatment Effects from Time-to-Event Data](https://mlsanity.com/paper/2110.14001/) (2021)
- [Evaluation Methods and Measures for Causal Learning Algorithms](https://mlsanity.com/paper/2202.02896/) (2022)
- [Conformal Meta-learners for Predictive Inference of Individual Treatment Effects](https://mlsanity.com/paper/2308.14895/) (2023)
- [Robust and Agnostic Learning of Conditional Distributional Treatment Effects](https://mlsanity.com/paper/2205.11486/) (2022)
- [TabPFN: One Model to Rule Them All?](https://mlsanity.com/paper/2505.20003/) (2025)
- [Comparison of meta-learners for estimating multi-valued treatment heterogeneous effects](https://mlsanity.com/paper/2205.14714/) (2022)
- [A Survey of Deep Causal Models and Their Industrial Applications](https://mlsanity.com/paper/2209.08860/) (2022)
- [An Efficient Doubly-Robust Test for the Kernel Treatment Effect](https://mlsanity.com/paper/2304.13237/) (2023)
- [Estimating Potential Outcome Distributions with Collaborating Causal Networks](https://mlsanity.com/paper/2110.01664/) (2021)
- [Generalized Bayesian Additive Regression Trees Models: Beyond Conditional Conjugacy](https://mlsanity.com/paper/2202.09924/) (2022)
- [Identifiable Energy-based Representations: An Application to Estimating Heterogeneous Causal Effects](https://mlsanity.com/paper/2108.03039/) (2021)
- [Stochastic Tree Ensembles for Estimating Heterogeneous Effects](https://mlsanity.com/paper/2209.06998/) (2022)
- [A Mixing Time Lower Bound for a Simplified Version of BART](https://mlsanity.com/paper/2210.09352/) (2022)
- [Proximal Causal Learning of Conditional Average Treatment Effects](https://mlsanity.com/paper/2301.10913/) (2023)
- [Covariate-Balancing-Aware Interpretable Deep Learning models for Treatment Effect Estimation](https://mlsanity.com/paper/2203.03185/) (2022)
- [Minimax Regret Estimation for Generalizing Heterogeneous Treatment Effects with Multisite Data](https://mlsanity.com/paper/2412.11136/) (2024)
- [Meta-Learners for Estimation of Causal Effects: Finite Sample Cross-Fit Performance](https://mlsanity.com/paper/2201.12692/) (2022)
- [Bayesian Safe Policy Learning with Chance Constrained Optimization: Application to Military Security Assessment during the Vietnam War](https://mlsanity.com/paper/2307.08840/) (2023)
- [Uncertainty Quantification in Heterogeneous Treatment Effect Estimation with Gaussian-Process-Based Partially Linear Model](https://mlsanity.com/paper/2312.10435/) (2023)
- [Hybrid Meta-learners for Estimating Heterogeneous Treatment Effects](https://mlsanity.com/paper/2506.13680/) (2025)
- [GCF: Generalized Causal Forest for Heterogeneous Treatment Effect Estimation in Online Marketplace](https://mlsanity.com/paper/2203.10975/) (2022)
- [Assisting Clinical Decisions for Scarcely Available Treatment via Disentangled Latent Representation](https://mlsanity.com/paper/2307.03315/) (2023)
- [Practical Marketplace Optimization at Uber Using Causally-Informed Machine Learning](https://mlsanity.com/paper/2407.19078/) (2024)
- [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)
- [Doubly Robust Kernel Statistics for Testing Distributional Treatment Effects](https://mlsanity.com/paper/2212.04922/) (2022)
- [Heterogeneous Synthetic Learner for Panel Data](https://mlsanity.com/paper/2212.14580/) (2022)
- [Fairness Implications of Heterogeneous Treatment Effect Estimation with Machine Learning Methods in Policy-making](https://mlsanity.com/paper/2309.00805/) (2023)

## Abstract (arXiv)

Hahn et al. (2020) offers an extensive study to explicate and evaluate the performance of the BCF model in different settings and provides a detailed discussion about its utility in causal inference. It is a welcomed addition to the causal machine learning literature. I will emphasize the contribution of the BCF model to the field of causal inference through discussions on two topics: 1) the difference between the PS in the BCF model and the Bayesian PS in a Bayesian updating approach, 2) an alternative exposition of the role of the PS in outcome modeling based methods for the estimation of causal effects. I will conclude with comments on avenues for future research involving BCF that will be important and much needed in the era of Big data.