# A Bayesian Semiparametric Method For Estimating Causal Quantile Effects

arXiv: https://arxiv.org/abs/2211.01591 · HTML: https://mlsanity.com/paper/2211.01591/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 46 references that are in the map.
- First posted on arXiv 3 Nov 2022.

## Builds on (most cited first, 11 of 11)

- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [Bayesian Neural Network Priors Revisited](https://mlsanity.com/paper/2102.06571/) (2021)
- [Model Selection in Bayesian Neural Networks via Horseshoe Priors](https://mlsanity.com/paper/1705.10388/) (2017)
- [Semiparametric counterfactual density estimation](https://mlsanity.com/paper/2102.12034/) (2021)
- [Estimating Individual Treatment Effect in Observational Data Using Random Forest Methods](https://mlsanity.com/paper/1701.05306/) (2017)
- [Nonparametric Conditional Density Estimation in a High-Dimensional Regression Setting](https://mlsanity.com/paper/1604.00540/) (2016)
- [Causal effects based on distributional distances](https://mlsanity.com/paper/1806.02935/) (2018)
- [Informative Bayesian Neural Network Priors for Weak Signals](https://mlsanity.com/paper/2002.10243/) (2020)
- [Robust inference of conditional average treatment effects using dimension reduction](https://mlsanity.com/paper/2008.13137/) (2020)
- [Bayesian Non-parametric Quantile Process Regression and Estimation of Marginal Quantile Effects](https://mlsanity.com/paper/2102.11309/) (2021)
- [Causal Inference for Quantile Treatment Effects](https://mlsanity.com/paper/2109.03757/) (2021)

## Abstract (arXiv)

Standard causal inference characterizes treatment effect through averages, but the counterfactual distributions could be different in not only the central tendency but also spread and shape. To provide a comprehensive evaluation of treatment effects, we focus on estimating quantile treatment effects (QTEs). Existing methods that invert a nonsmooth estimator of the cumulative distribution functions forbid inference on probability density functions (PDFs), but PDFs can reveal more nuanced characteristics of the counterfactual distributions. We adopt a semiparametric conditional distribution regression model that allows inference on any functionals of counterfactual distributions, including PDFs and multiple QTEs. To account for the observational nature of the data and ensure an efficient model, we adjust for a double balancing score that augments the propensity score with individual covariates. We provide a Bayesian estimation framework that appropriately propagates modeling uncertainty. We show via simulations that the use of double balancing score for confounding adjustment improves performance over adjusting for any single score alone, and the proposed semiparametric model estimates QTEs more accurately than other semiparametric methods. We apply the proposed method to the North Carolina birth weight dataset to analyze the effect of maternal smoking on infant's birth weight.