Whenever the frequency of an event of interest is extremely low — such as with acts of terrorism — even a very accurate test will fail very often. Corey Chivers explains why.

Recent revelations about PRISM, the NSA’s massive program of surveillance of civilian communications have caused quite a stir. And rightfully so, as it appears that the agency has been granted warrantless direct access to just about any form of digital communication engaged in by American citizens, and that their access to such data has been growing significantly over the past few years.

Some may argue that there is a necessary trade-off between civil liberties and public safety, and that others should just quit their whining. Lets take a look at this proposition (not the whining part). Specifically, let’s ask: how much benefit, in terms of thwarted would-be attacks, does this level of surveillance confer?

Lets start by recognizing that terrorism is extremely rare. So the probability that an individual under surveillance (and now everyone is under surveillance) is also a terrorist is also extremely low. Lets also assume that the neck-beards at the NSA are fairly clever, if exceptionally creepy. We assume that they have devised an algorithm that can detect ‘terrorist communications’ (as opposed to, for instance, pizza orders) with 99% accuracy.

P(+ | bad guy) = 0.99

A job well done, and Murica lives to fight another day. Well, not quite. [Continue reading…]