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We consider a a collection of categorical random variables. Of specialinterest is the causal effect on an outcome variable following an interventionon another variable. Conditionally on a Directed Acyclic Graph (DAG), we assumethat the joint law of the random variables can be factorized according to theDAG, where each term is a categorical distribution for the node-variable givena configuration of its parents. The graph is equipped with a causalinterpretation through the notion of interventional distribution and the allied"do-calculus". From a modeling perspective, the likelihood is decomposed into aproduct over nodes and parents of DAG-parameters, on which a suitably specifiedcollection of Dirichlet priors is assigned. The overall joint distribution onthe ensemble of DAG-parameters is then constructed using global and localindependence. We account for DAG-model uncertainty and propose a reversiblejump Markov Chain Monte Carlo (MCMC) algorithm which targets the jointposterior over DAGs and DAG-parameters; from the output we are able to recovera full posterior distribution of any causal effect coefficient of interest,possibly summarized by a Bayesian Model Averaging (BMA) point estimate. Wevalidate our method through extensive simulation studies, wherein comparisonswith alternative state-of-the-art procedures reveal an outperformance in termsof estimation accuracy. Finally, we analyze a dataset relative to a study ondepression and anxiety in undergraduate students.

Joint structure learning and causal effect estimation for categorical graphical models