Title: Learning procedure for chain (stratified) graphical models
Authors: Manuela Cazzaro - University of Milano-Bicocca (Italy) [presenting]
Federica Nicolussi - University of Milan (Italy)
Agnese Maria Di Brisco - University of Milano Bicocca (Italy)
Abstract: The analysis and modeling of multivariate categorical data, usually summarized as contingency tables, is an open issue in statistics. Graphical models are powerful statistical tools to quantify the structure of dependence of these data. Interestingly, the system of (in)dependencies can be represented through a graphical representation such that each vertex of the graph corresponds to a variable and the presence (absence) of an arc between a couple of vertices indicates their functional dependence (independence). Moreover, standard graphical models have been extended to chain stratified graphical models to allow for a greater flexibility in terms of model structure (i.e., permitting marginal, conditional and context-specific independences simultaneously). Several methods exist for Bayesian model determination, i.e. Bayesian learning, of graphical models. In this regard, the first aim is to define a new algorithm of Bayesian learning along the path set out previously. A further aim is to extend the latter algorithm to chain stratified graphical models, thus accounting for context-specific independences. Intensive simulation studies are performed to evaluate the performance of the proposed algorithms and to compare them with existing methods of Bayesian learning.