## 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 *P*_{A}, 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 *P*_{A} 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
*P*_{A} = 1 is simply that an evaluation of
*P*_{A} 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;t*_{0}) =
*P(t*_{0}|*t)* = probability that the
observation that the event has never occurred took place at or
before time *t*_{0}, given that the time of first
occurrence is *t* taken as the uniform distribution
*t*_{0}/*t* (for *t*_{0}
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.