The revision of elicited beliefs on the structure of a Bayesian Network
Federico Mattia Stefanini · Florence Research (University of Florence) · 2009
In the last ten years, a few graphical models have been developed and successfully applied to bioinformatics-related fields like gene expression, proteomics and metabolomics. In these fields the elicitation of prior information may play several roles. It is a resource against the curse of dimensionality which affects high dimensional multivariate models, especially with moderate or low sample size. Moreover it leads the expert to avoid shallow thinking and the use of blind numerical procedures by encouraging deep thinking towards meaningful models. In a recent contribution from the literature on score-based (Bayesian) structural learning of Bayesian networks it has been proposed an elicitation procedure focused on “network features”, a collection of propositions characterizing a-priori plausible structures. The proposed approach is sensible both in addressing the possible lack of detailed expert information in a huge space of candidate structures and in reducing the super-exponential number of values otherwise to be elicited. Moreover several limitations of other approaches are avoided, like the need of a total ordering of nodes, the presence of sharp constraints, the marginal independence of unknowns or the existence of a prior network that is a good summary of expert prior beliefs. In this work we introduce a parameterization derived from log-linear models where variables indicate the presence/absence of reference features. We show that the parameterization may be useful both to assist the expert in the revision of an elicited distribution or in the elicitation of beliefs characterized by the lack of higher order interactions among reference features. A case study dealing with breast cancer and presented in the cited paper is reconsidered and elaborated to illustrate some features of the proposed parameterization. The discussion includes considerations on computing in view of the development of an open source Java package.