# Bayesian Inference and Partial Identification in Multi-Treatment Causal Inference with Unobserved Confounding

arXiv: https://arxiv.org/abs/2111.07973 · HTML: https://mlsanity.com/paper/2111.07973/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2021.

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

- [Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounders](https://mlsanity.com/paper/2303.02320/) (2023)
- [Bayesian X-Learner: Calibrated Posterior Inference for Heterogeneous Treatment Effects under Heavy-Tailed Outcomes](https://mlsanity.com/paper/2604.27394/) (2026)

## Abstract (arXiv)

In causal estimation problems, the parameter of interest is often only partially identified, implying that the parameter cannot be recovered exactly, even with infinite data. Here, we study Bayesian inference for partially identified treatment effects in multi-treatment causal inference problems with unobserved confounding. In principle, inferring the partially identified treatment effects is natural under the Bayesian paradigm, but the results can be highly sensitive to parameterization and prior specification, often in surprising ways. It is thus essential to understand which aspects of the conclusions about treatment effects are driven entirely by the prior specification. We use a so-called transparent parameterization to contextualize the effects of more interpretable scientifically motivated prior specifications on the multiple effects. We demonstrate our analysis in an example quantifying the effects of gene expression levels on mouse obesity.