Probabilistic interpretation of command and control signals: Bayesian updating of the probability of nuclear attack

A warning system such as the Command, Control, Communication, and Intelligence system (C3I) for the United States nuclear forces operates on the basis of various sources of information among which are signals from sensors. A fundamental problem in the use of such signals is that these sensors provide only imperfect information. Bayesian probability, defined as a degree of belief in the possibility of each event, is therefore a key concept in the logical treatment of the signals. However, the base of evidence for estimation of these probabilities may be small and, therefore, the results of the updating (posterior probabilities of attack) may also be uncertain. In this paper, we examine the case where uncertainties hinge upon the existence of several possible underlying hypotheses (or models), and where the decision-maker attributes a different probability of attack to each of these fundamental hypotheses. We present a two-stage Bayesian updating process, first of the probabilities of the fundamental hypotheses, then of the probabilities of attack conditional on each hypothesis, given a positive signal from the C3I. We illustrate the method in the discrete case where there are only two possible fundamental hypotheses, and in the case of a continuous set of hypotheses. We discuss briefly the implications of the results for decision-making. The method can be generalized to other warning systems with imperfect signals, when the prior probability of the event of interest is uncertain.