Bayesian networks were developed in the late 1970's to model distributed processing in reading comprehension, where both semantical expectations and perceptual evidence must be combined to form a coherent interpretation. The ability to coordinate bi-directional inferences lled a void in expert systems technology of the early 1980's, and Bayesian networks have emerged as a general representation scheme for uncertain knowledge [Pearl, 1988; Shafer and Pearl, 1990; Heckerman et al., 1995; Jensen, 1996; Castillo et al., 1997]. . Bayesian networks are directed acyclic graphs (DAGs) in which the nodes represent variables of interest (e.g., the temperature of a device, the gender of a patient, a feature of an object, the occurrence of an event) and the links represent informational or causal dependencies among the variables. The strength of a dependency is represented by conditional probabilities that are attached to each cluster of parents-child nodes in the network. Figure 1 illustrates a simple yet typical Bayesian network. It describes the causal relationships among the season of the year (X1), whether rain falls (X2) during the season, whether the sprinkler is on (X3) during that season, whether the pavement would get wet (X4), and whether the pavement would be slippery (X5). Here, the absence of a direct link between X1 and X5, for example, captures our understanding that the in uence of seasonal variations on the slipperiness of the pavement is mediated by other conditions (e.g., wetness).