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A1043
Title: Causal inference for categorical graphical models Authors:  Federico Castelletti - Università Cattolica del Sacro Cuore (Milan) (Italy)
Guido Consonni - Universita Cattolica del Sacro Cuore (Italy) [presenting]
Marco Della Vedova - Chalmers University of Technology Goteborg (Sweden)
Abstract: A collection of categorical random variables organized in a network is considered. The interest lies in the causal effect on an outcome variable following an intervention on another variable. Conditionally on a Directed Acyclic Graph (DAG), it is assumed that the joint distribution of the random variables can be factorized according to the DAG. The graph is equipped with a causal interpretation through the notion of interventional distribution and the allied do-calculus. The likelihood decomposes into a product of terms, each involving the probability of a node given its parent configurations; the prior, accordingly, is a product of suitably defined Dirichlet distributions. DAG-model uncertainty is taken into account, and a reversible jump MCMC algorithm proposed which targets the joint posterior over DAGs and DAG parameters; from the output, the full posterior distribution of any causal effect of interest is recovered, possibly summarized by a Bayesian Model Averaging (BMA) estimate. The method is validated through simulation studies, wherein the method outperforms alternative state-of-the-art procedures in terms of estimation accuracy. Finally, a dataset on depression and anxiety in undergraduate students is analyzed.