Estimating the likelihood of catastrophic events, and particularly terrorist attacks, is extremely important. But in general, these catastrophes are outliers in whatever situation we are looking at. So how can we make sure that any estimate for a rare event is accurate, robust, and meaningful?

In a recent paper posted to the arXiv, my friend and colleague Aaron Clauset, along with his collaborator Ryan Woodard, set out to use a sophisticated statistical approach to address this problem. They first note two difficulties:

(i) we typically lack quantitative mechanism-based models with demonstrated predictive power at the global scale (which is particularly problematic for CBRN [chemical, biological, radioactive or nuclear] events) and (ii) the global historical record contains few large events from which to estimate mechanism-agnostic statistical models of large events alone. That is, the rarity of big events implies large fluctuations in the distribution’s upper tail, precisely where we wish to have the most accuracy.

So how do they handle this? Their method does not attempt to provide a detailed generative model. Rather their approach combines numerous sophisticated statistical techniques in order to handle the large amount of uncertainty inherent in making these types of predictions. And it mainly comes down to finding a model to fit the “tail” of the distribution, the right-hand portion of the distribution that deals with the likelihood of rare events: