Manhunting by Numbers

One of the many pieces of bin Laden-related trivia in the news today is the resuscitation of a study by a group of geographers at UCLA, published in 2009, which according to the BBC ‘said there was a high probability Osama Bin Laden was located in the town where he was ultimately killed by US operatives on Sunday'. The BBC report goes on:

The model employed in the study, which is typically used to track endangered species, said there was a 88.9 per cent chance he was in Abbottabad in Pakistan.

But geographer Thomas Gillespie at UCLA said the same study gave a 95 per cent chance he was in another town, Parachinar.

There's clearly something amiss here: if there was an 88.9 per cent chance he was in Abbottabad, there could only have been an 11.1 per cent chance he was anywhere else. Puzzled, I asked a statistician how the numbers could add up, and he said:

Either they don’t mind him being in more than one place or they aren’t using probability. I think, in effect, they are assigning numbers to hypotheses to indicate a degree of belief and doing clever stuff with the numbers to work out which hypothesis is the most believable but being careless in describing the numbers as probabilities. The term ‘probability’ ought to be reserved for numbers that behave in a particular mathematical way, and these won’t.

The magic number – 88.9 per cent – has been quoted in just about every version of the report that I've seen, which isn't very surprising since they all seem to derive from the same source, a story published in Science a couple of days ago, which now has a disclaimer at the end:

This item has been corrected. The figure initially reported was incorrect; the model predicted a 88.9 per cent probability given the distance. Also, the model only predicts the probability of his being within a geographic radius of his last known location, not a specific city. The article has been corrected to reflect this fact.

But many of the articles based on it haven't.

The appeal of such a precise figure to journalists (or 88.9 per cent of them, anyway) is obvious: nothing like a few numbers, especially ones with a decimal point, to wow the laity. Never mind that the researchers' argument is far easier to follow when the numbers are left out of it:

Distance-decay theory would predict that he is closest to the point where he was last reported and, by extension, within a region that has a similar physical environment and cultural composition (that is, similar religious and political beliefs)... Island biogeographic theory predicts that bin Laden is in a larger town rather than a smaller and more isolated town where extinction rate would be higher. Finally, high-resolution analyses of a city can be undertaken to identify individual buildings that match bin Laden’s life history characteristics.

Put like that, it isn't rocket science. It isn't even weather forecasting. As Gillespie would probably be the first to admit. 'Right now, I’m working on the dry forests of Hawaii where 45 per cent of the trees are on the endangered species list,' he told Science. 'I’m far more interested in getting trees off the endangered species list.'