1Introduction Bayesian networks are widely accepted in Artificial Intelligence research as intuitively appealing, practical representations of knowledge for reasoning under uncertainty and for putting causal models on a solid mathematical basis [72]. They are also referred to as belief networks [82] (chapter 15), causal networks [73] and decision networks or influence diagrams [48] when combined with decision theory. As computers become more powerful, Bayesian networks are being seen more in use in real life applications in many domains including fault diagnosis [41], medical diagnosis [70, 71, 97], forecasting [1, 20], vision [84], sensor fusion [6], software debugging [43], knowledge discovery and data mining [39], user modelling [16, 47] and software testing [113].
A Bayesian Network (BN) is a representation of a joint probability distribution on a set of statistical variables. It consists of a qualitative part (a ‘graphical structure’, a ‘graph’ or a ‘structure’) and an associated quantitative part (the parameters, the numbers). The graph structure in a BN is a Directed Acyclic Graph (DAG) and formally represents the structural assumptions of the domain, i.e., what concepts (variables) the domain is comprised of, what values they can take (the partition of these variables) and what are the (dependenceindependence) relationships between the concepts (variables). Helsper and van der Gaag [44] suggest the use of ontology to capture all structural assumptions (as well as metalevel knowledge) from which, in a sequence of steps addressing graphical modelling issues, several alternative graphical structures can be derived. Graphical Modelling is the construction of the graph according to such structural assumptions about the domain, based on the syntax of BNs. Graphical modelling decisions include: choosing the relevant concepts, translating them into variables, and deciding on their states and the relationships between them. Each node in the graph represents one of the variables; an arc between two nodes represents possible dependence between the two variables and the absence of an arc between two nodes represents conditional independence between the two variables. The quantitative part associates with each node a conditional probability table (CPT) that encodes the strength of the dependency between the node and the nodes that are connected to it (its parents). Once the qualitative and the quantitative parts are defined, new probabilities of unknown variables can be calculated from known variables. This mechanism is called inference.
Ample research, literature and tool support, have focused on inference algorithms, obtaining the CPTs and assessing the numbers by examining how the model matches experts’ expectations. By contrast, the acquisition and the assessment of the graph structure have received much less attention. It has long been accepted that for the purpose of eliciting the graphical modelling decisions the formal notions of directional conditional independency can be replaced by informal notions of causation and influence, and the considerations can be kept locally [72] (p. 123124). This is thought to enable people to express their knowledge intuitively when constructing the graph. However, recently it has been argued that this approach is too simplistic [44, 58] and, in fact, the way a graph represents knowledge is far from being obvious to someone who is inexperienced in BN technology. Mistakes can be made in the graph construction, which may not be obvious to the domain expert (DE) but can have crucial effects on the model construction, maintenance, accuracy and tractability [26, 58]. For example, the intuitive construction of a causative network, although very useful, can be a source of such mistakes. Current tools and literature do not provide sufficient support to the DEs in constructing their networks and identifying potential errors therein. In particular, they necessitate the definition of the quantitative part. Therefore DEs need to be supported by BN experts to reduce potential problems [26, 58].
