# Bayesian analysis of regression discontinuity designs with heterogeneous treatment effects

arXiv: https://arxiv.org/abs/2504.10652 · HTML: https://mlsanity.com/paper/2504.10652/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2025.

## Built on by (most cited first, 2 of 2)

- [Causal Inference under Threshold Manipulation: Bayesian Mixture Modeling and Heterogeneous Treatment Effects](https://mlsanity.com/paper/2509.19814/) (2025)
- [Direct Bayesian Additive Regression Trees for Conditional Average Treatment Effects in Regression Discontinuity Designs](https://mlsanity.com/paper/2603.03819/) (2026)

## Abstract (arXiv)

Regression Discontinuity Design (RDD) is a popular framework for estimating a causal effect in settings where treatment is assigned if an observed covariate exceeds a fixed threshold. We consider estimation and inference in the common setting where the sample consists of multiple known sub-populations with potentially heterogeneous treatment effects. In the applied literature, it is common to account for heterogeneity by either fitting a parametric model or considering each sub-population separately. In contrast, we develop a Bayesian hierarchical model using Gaussian process regression which allows for non-parametric regression while borrowing information across sub-populations. We derive the posterior distribution, prove posterior consistency, and develop a Metropolis-Hastings within Gibbs sampling algorithm. In extensive simulations, we show that the proposed procedure outperforms existing methods in both estimation and inferential tasks. Finally, we apply our procedure to U.S. Senate election data and discover an incumbent party advantage which is heterogeneous over different time periods.