Graph-Split Bayesian Causal Forest for Spatial Heterogeneous Treatment Effect Estimation
Abstract
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.
Related
- Factorial Multivariate Bayesian Causal Forests: heterogeneous main and interaction effects of multiple treatments on correlated outcomes
- Explaining Heterogeneous Treatment Effects with Causal Forests and the Hoeffding Functional Decomposition
- Amortized Bayesian Disease Mapping and Boundary Detection on Heterogeneous Spatial Graphs
- Is the treatment beneficial? Causal Inference with Ordinal Outcomes: A Bayesian Solution
- Global minimax rates for heterogeneous treatment effect estimation
BibTeX
@misc{he2026graphsplit,
title = {{Graph-Split Bayesian Causal Forest for Spatial Heterogeneous Treatment Effect Estimation}},
author = {Shuren He and Huiyan Sang and Ligang Lu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36046},
eprint = {2609.36046},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36046},
}
RIS
TY - UNPB
TI - Graph-Split Bayesian Causal Forest for Spatial Heterogeneous Treatment Effect Estimation
AU - Shuren He
AU - Huiyan Sang
AU - Ligang Lu
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36046
UR - https://arxiv.org/abs/2609.36046
AB - 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.
ER -