Prior and posterior checking of implicit causal assumptions.

Area of Science:

• Causal Inference
• Machine Learning
• Bayesian Statistics

Background:

• Machine learning and Bayesian nonparametrics are increasingly used for causal effect uncertainty quantification.
• High-dimensional Bayesian models may unintentionally encode prior information that downplays confounding.

Purpose of the Study:

• To identify and address the issue of prior distributions in Bayesian causal inference unintentionally minimizing confounding.
• To provide tools for verifying prior and posterior distributions in the context of confounding.

Main Methods:

• Developing methods to verify if prior distributions exhibit inductive bias against confounded models.
• Assessing if posterior distributions contain adequate information to overcome potential prior biases.
• Proof-of-concept on simulated high-dimensional probit-ridge regression data.
• Illustration using a Bayesian nonparametric decision tree ensemble on medical expenditure survey data.

Main Results:

• Demonstrated how regularization in high-dimensional Bayesian models can imply negligible confounding.
• Provided practical tools to diagnose and mitigate prior-induced biases in causal inference.
• Showcased the utility of the proposed methods on both simulated and real-world data.

Conclusions:

• Bayesian nonparametric methods offer flexibility but require careful prior specification in causal inference.
• The developed tools aid practitioners in ensuring the validity of uncertainty quantification for causal effects.
• Addressing prior biases is crucial for reliable causal effect estimation in high-dimensional settings.