# Graph-Split Bayesian Causal Forest for Spatial Heterogeneous Treatment Effect Estimation

arXiv: https://arxiv.org/abs/2609.36046 · HTML: https://mlsanity.com/paper/2609.36046/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 28 Sep 2026.

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

- [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)
- [Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets](https://mlsanity.com/paper/1406.7343/) (2014)
- [Balancing Covariates via Propensity Score Weighting](https://mlsanity.com/paper/1609.07494/) (2016)
- [Gaussian Process Boosting](https://mlsanity.com/paper/2004.02653/) (2020)
- [A review of spatial causal inference methods for environmental and epidemiological applications](https://mlsanity.com/paper/2007.02714/) (2020)
- [Neural networks for geospatial data](https://mlsanity.com/paper/2304.09157/) (2023)
- [Adjusting for Unmeasured Spatial Confounding with Distance Adjusted Propensity Score Matching](https://mlsanity.com/paper/1610.07583/) (2016)
- [Generalized propensity score approach to causal inference with spatial interference](https://mlsanity.com/paper/2007.00106/) (2020)
- [Stochastic Tree Ensembles for Estimating Heterogeneous Effects](https://mlsanity.com/paper/2209.06998/) (2022)
- [Bayesian Nonparametric Space Partitions: A Survey](https://mlsanity.com/paper/2002.11394/) (2020)
- [On Mixing Rates for Bayesian CART](https://mlsanity.com/paper/2306.00126/) (2023)
- [PSweight: An R Package for Propensity Score Weighting Analysis](https://mlsanity.com/paper/2010.08893/) (2020)
- [Inferring Heterogeneous Causal Effects in Presence of Spatial Confounding](https://mlsanity.com/paper/1901.09919/) (2019)
- [GS-BART: Bayesian Additive Regression Trees with Graph-split Decision Rules](https://mlsanity.com/paper/2509.07166/) (2025)

## Abstract (arXiv)

In spatial observational studies, treatment assignment and outcomes often exhibit spatial dependence patterns, and treatment effects may vary across space and subpopulations due to both measured and unmeasured spatially structured confounders. Accounting for spatial dependence while estimating heterogeneous treatment effects (HTEs) is a central task in spatial causal inference. Causal Bayesian additive regression tree methods are popular nonparametric methods for modeling and estimating HTEs. Despite their flexibility and uncertainty quantification, the axis-aligned split rules often adopted in these models are not suitable for modeling spatial structures. We propose a spatial structure-aware Bayesian nonparametric method, called Graph-Split Bayesian Causal Forest (GSBCF), that integrates graph-split Bayesian additive regression trees (GS-BART) with the Bayesian causal forest propensity-score regression framework for spatial heterogeneous causal inference. Spatial confounding is accommodated through graph-guided split rules in modeling decision trees of the prognostic and HTE functions. We develop an efficient informed proposal sampling algorithm for posterior computation, enabling full Bayesian inference of the spatial conditional average treatment effect function. Simulations and a real data study demonstrate substantially improved estimation accuracy and uncertainty quantification over existing causal BART methods.