Bayesian Updating of the Probability of Nuclear Attack

A warning system such as the Command, Control, Communications, and Intelligence system (C3I) for the U.S. nuclear forces operates on the basis of various sources of information, among which are signals from sensors. These sensors include, for example, radar receivers and satellites. A fundamental problem in the use of such signals is that the sensors provide only imperfect information. Two kinds of errors are possible: missed signals (Type I errors) and false alerts (Type II errors). Probability is therefore a key concept in the logical treatment of such signals. It is defined, in the Bayesian sense, as a degree of belief in the possibility ofeach event (in this case, attack or no attack, signal or no signal, and action or no action) (Savage 1954). One of the main problems in the use of the Bayesian method is that, because the base of evidence for estimation of these probabilities may be small, the figures may be fuzzy. A first issue is thus how to account, using probabilities, for the primary uncertainties about signals and events. A second issue is how to assess and treat uncertainties about these probabilities (epistemic uncertainties) while preserving probabilistic logic. A third issue is the relevance of these epistemic uncertainties in rational and prudent decision making when the stakes are as high as the possibility of an accidental nuclear attack.