A practical introduction to Bayesian estimation of causal effects: Parametric and nonparametric approaches

Area of Science:

• Statistics
• Causal Inference
• Bayesian Methods

Background:

• Recent years have seen significant advancements in Bayesian methodologies for causal inference.
• Practicing statisticians with existing Bayesian model familiarity can benefit from understanding causal estimation enhancements.
• Bayesian approaches offer unique advantages for addressing complex causal questions in various settings.

Purpose of the Study:

• To introduce Bayesian inference for causal effects to statisticians.
• To demonstrate the utility of Bayesian methods in practical causal estimation.
• To provide implementation-level knowledge of both parametric and nonparametric Bayesian causal inference.

Main Methods:

• Utilizing priors for shrinkage and sparsity in parametric causal models.
• Performing probabilistic sensitivity analyses for causal assumptions.
• Overviewing nonparametric Bayesian estimation techniques and their causal inference applications.
• Considering both point-treatment and time-varying treatment (static and dynamic) settings.

Main Results:

• Demonstration of how Bayesian priors can regularize parametric models for improved causal estimates.
• Illustration of probabilistic sensitivity analysis for robust causal conclusions.
• Survey of nonparametric Bayesian methods applied to causal inference problems.
• Practical implementation guidance using open-source software.

Conclusions:

• Bayesian causal inference provides a flexible and powerful framework for statistical estimation.
• The presented methods, including parametric and nonparametric approaches, are readily implementable.
• Publicly available code and examples facilitate the adoption of these Bayesian causal inference techniques.