Suitable Prior Distributions for Additive Bayesian Networks Models

• Activity Number: 313
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Marta Pittavino* and Reinhard Furrer
• Companies: University of Zurich and University of Zurich
• Keywords: Conjugacy property ; Graphical models ; Generalized linear models ; Independence and likelihood equivalence assumptions ; Marginal likelihood computation ; Posterior parameter estimation

Abstract

Bayesian networks (BNs) are a form of graphical model which derives from empirical data a directed acyclic graph describing the dependency structure between random variables. Additive Bayesian networks (ABNs) consist of a special type of graphical model that generalize the usual generalized linear models to multiple dependent variables without involving dimension reduction. The result of fitting an ABN to a data set is translated into the likelihood of observing the data under the studied model: the marginal likelihood. We introduce a novel conjugate prior distribution for ABNs models that help us to address the posterior parameter estimation and the goodness of fit computation. Independence (each node can be considered separately) and likelihood equivalence (data should not help to discriminate network structures that represent the same assertions of conditional independence) are crucial assumptions for BNs models. We discuss and show the implications of these assumptions for ABNs models with our conjugate prior. We demonstrate with an applied example the computational advantages gained from our prior's choice to compute the posterior parameters and the marginal likelihoods.