Abstract

The increasing availability of high-quality official statistics data offers new opportunities for multivariate statistical modelling and the investigation of complex dependence structures. In this context, Bayesian networks (BNs) provide a powerful and flexible framework, with structure learning representing a crucial step in their construction. However, conventional BN structure learning methods typically assume independent and identically distributed observations, an assumption that is generally not satisfied by data collected through complex sampling designs.
Stratification, clustering, and unequal inclusion probabilities pose important methodological challenges, as ignoring the sampling design may affect score-based model selection and the resulting network structure.
This work addresses these challenges by proposing a survey-weighted Bayesian Information Criterion (BIC) for BN structure learning. The classical log-likelihood is replaced by a weighted pseudo-log-likelihood, and the complexity penalty is adjusted to account for the sampling design. Two alternative criteria are considered: a node-specific penalty based on design effects derived from a variance-to-curvature ratio, for which consistency is established, and a simplified criterion based on an effective sample size incorporating a common design effect. Their performance is investigated through a simulation study.
The performance of the proposed methodology is investigated through a simulation study and illustrated with an application to European Social Survey (ESS) data.
This is joint work with Daniela Marella (Sapienza University, Rome) and Flaminia Musella (University Roma Tre, Rome).