PNNL

Abstract

Bayesian networks have attained widespread use in data analysis and decision making. Well studied topics include: efficient inference, evidence propagation, parameter learning from data for complete and incomplete data scenarios, expert elicitation for calibrating Bayesian network probabilities, and structure learning. It is not uncommon for the researcher to assume the structure of the Bayesian network or to glean the structure from expert elicitation or domain knowledge. In this scenario, the model may be calibrated through learning the parameters from relevant data. There is a lack of work on model diagnostics for fitted Bayesian networks; this is the contribution of this paper. We key on the definition of (conditional) independence to develop a graphical diagnostic method which indicates if the conditional independence assumptions imposed when one assumes the structure of the Bayesian network are supported by the data. We develop the approach theoretically and describe a Monte Carlo method to generate uncertainty measures for the consistency of the data with conditional independence assumptions under the model structure. We describe how this theoretical information and the data are presented in a graphical diagnostic tool. We demonstrate the approach through data simulated from Bayesian networks under different conditional independence assumptions. We also apply the diagnostic to a real world data set. The results indicate that our approach is a reasonable way of visualizing and inspecting the conditional independence assumption of a Bayesian network given data.