Agenda

Guido Consonni - Università Cattolica del Sacro Cuore, Milano

Titolo completo: Bayesian inference of causal effects from observational data in Gaussian graphical models

Abstract: We assume that multivariate observational data are generated from a distribution whose conditional independencies are encoded in a Directed Acyclic Graph (DAG). For any given DAG, the causal effect of a variable onto another one can be evaluated through intervention calculus. A DAG is typically not identifiable from observational data alone. However its Markov equivalence class (a collection of DAGs) can be estimated from the data. As a consequence, for the same intervention a set of causal effects, one for each DAG in the equivalence class, can be evaluated. In this paper we propose a fully Bayesian methodology to make inference on the causal effects of any intervention in the system. Main features of our method are: i) both uncertainty on the equivalence class and the causal effects are jointly modeled; ii) priors on the parameters of the modified Cholesky decomposition of the precision matrices across all DAG models are constructively assigned starting from a unique prior on the complete (unrestricted) DAG; iii) an efficient algorithm to sample from the posterior distribution on graph space is adopted; iv) an objective Bayes approach, requiring virtually no user specification, is used throughout. We demonstrate the merits of our methodology in simulation studies, wherein comparisons with current state-of-the-art procedures turns out to be highly satisfactory. Finally we examine a real data set of gene expressions for Arabidopsis thaliana. This is joint work with Federico Castelletti.