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

TL;DR

This paper explores Bayesian methods for estimating treatment effects in multi-treatment causal inference with unobserved confounding, emphasizing the influence of prior choices and using transparent parameterization to interpret results.

Contribution

It introduces a transparent parameterization approach to analyze the sensitivity of Bayesian inferences to prior specifications in partially identified causal models.

Findings

Bayesian inference can be highly sensitive to prior choices.

Transparent parameterization helps interpret prior influence.

Application to gene expression and obesity demonstrates practical relevance.

Abstract

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.