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.
翻译:在因果估算问题中,通常只是部分地确定了相关参数,这意味着即使有无限的数据也无法完全恢复该参数。在这里,我们研究了巴伊西亚在多处理因果推断问题中部分确定治疗效果的推论。原则上,根据巴伊西亚模式,部分确定治疗效果的推论是自然的,但结果对于参数化和先前的规格可能非常敏感,往往令人吃惊。因此,必须了解关于治疗效果的结论的哪些方面完全由先前的规格驱动。我们使用所谓的透明参数化来将更具有科学动机的先前规格对多重效应的影响背景化。我们用一个量化基因表达水平对鼠标肥胖的影响的示例来展示我们的分析。