Bayesian inference of causal effects from observational data in Gaussian graphical models.

Area of Science:

• Causal inference
• Statistical modeling
• Machine learning

Background:

• Observational data often implies conditional independencies representable by Directed Acyclic Graphs (DAGs).
• Causal effects can be assessed via intervention calculus for a given DAG.
• DAGs are not uniquely identifiable from observational data; Markov equivalence classes are estimated instead.

Purpose of the Study:

• To propose a fully Bayesian methodology for inferring causal effects of interventions.
• To jointly model uncertainty in Markov equivalence classes and causal effects.
• To provide an objective Bayesian approach with minimal user specification.

Main Methods:

• A novel Bayesian framework is developed for causal effect inference.
• Priors are assigned to precision matrix parameters across DAG models.
• An efficient algorithm samples from the posterior distribution on graph space.

Main Results:

• The proposed methodology jointly models uncertainty in equivalence classes and causal effects.
• Simulation studies show highly satisfactory performance compared to state-of-the-art methods.
• The approach is validated on a real-world gene expression dataset from Arabidopsis thaliana.

Conclusions:

• The Bayesian methodology offers a comprehensive approach to causal inference from observational data.
• It effectively handles uncertainty in graph structure and causal effect estimation.
• The method demonstrates practical utility in biological data analysis.