In spite of their remarkable power and potential to address inferential processes, there are some inherent limitations and liabilities to Bayesian networks.

In reviewing the Lumiere project, one potential problem that is seldom recognized is the remote possibility that a system's user might wish to violate the distribution of probabilities upon which the system is built. While an automated help desk system that is unable to embrace unusual or unanticipated requests is merely frustrating, an automated navigation system that is unable to respond to some previously unforeseen event might put an aircraft and its occupants in mortal peril. While these systems can update their goals and objectives based on prior distributions of goals and objectives among sample groups, the possibility that a user will make a novel request for information in a previously unanticipated way must also be accommodated.

Two other problems are more serious. The first is the computational difficulty of exploring a previously unknown network. To calculate the probability of any branch of the network, all branches must be calculated. While the resulting ability to describe the network can be performed in linear time, this process of network discovery is an NP-hard task which might either be too costly to perform, or impossible given the number and combination of variables.

The second problem centers on the quality and extent of the prior beliefs used in Bayesian inference processing. A Bayesian network is only as useful as this prior knowledge is reliable. Either an excessively optimistic or pessimistic expectation of the quality of these prior beliefs will distort the entire network and invalidate the results. Related to this concern is the selection of the statistical distribution induced in modelling the data. Selecting the proper distribution model to describe the data has a notable effect on the quality of the resulting network.