Non-destructive interrogation systems designed to locate illicit substances in sealed containers involve decision making when the available objective information is incomplete. The greater the quantity of information, the more reliable is the determination of the unknown content. Therefore, it is important to be able to utilize all possible measured data pertaining to the unknown object. Among the data which can be considered are x-ray measurements, fast-neutron transmission measurements, cargo manifest data and, possibly, information of a physical, chemical or even psychological nature. The Bayesian approach provides a statistical framework for merging diverse information about any object, including a priori knowledge, subjective knowledge and objective knowledge gained from current measurements. This paper outlines the fundamental principles of Bayesian analysis and explores possible applications to the detection of illicit substances.