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Citation:

K.T. Nelson, P. Nelson, "Probability of Attempted Armed Theft of Nuclear Weapons: Application of the Method of Gott," Proceedings of the INMM 52nd Annual Meeting, Palm Desert, CA, July 17-21, 2011.

Abstract:

A factor in the risk equation is PA, the probability per unit time that an attack occurs. This factor often is set to one, which is tantamount to evaluating the risk conditional upon an attack occurring. For some purposes (e.g., comparison of different defense strategies at a given site) this approach is quite adequate. For other purposes it has some deficiencies. (Two examples: Optimal allocation of resources between different sites for which PA might reasonably be expected not to be the same; and any effort to take account of attempts to deter attacks from occurring.) Perhaps an additional reason for often adopting the default value PA = 1 is simply that an evaluation of PA is difficult. (In this context it has even been stated that "deterrence is impossible to quantify.") This is an instance of the general difficulty of estimating the probability of occurrence of rare events. The extreme is an event that has never occurred. There is, in fact, a robust literature on the estimation of the probability of occurrence of events that have never occurred, beginning from a 1993 paper of Gott (J. Gott, III, "Implications of the Copernican Principle for our future prospects." Nature, 363, pp. 315-319 (1993)). This paper applies the approach of Gott to estimating the future probability of an attempted armed theft of US nuclear weapons, under the assumption that such an attempt has never occurred. At its heart the Gott approach is Bayesian, with the likelihood function L(t;t0) = P(t0|t) = probability that the observation that the event has never occurred took place at or before time t0, given that the time of first occurrence is t taken as the uniform distribution t0/t (for t0 between zero and t), where times are denominated from the first possibility of such an attempt (~1947). Results are illustrated for an exponential prior, with various values of the associated constant frequency. Specifically, differences between prior and posterior values of the pdf, cdf, time-dependent frequency and various quantiles for the probability of attempted thefts are displayed, for a range of values of the prior frequency.



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