Tuesday, May 03, 2011

An exercise in probability

One of Bin Laden’s wives identified his body, American officials said. A picture taken by a Seals commando and processed through facial recognition software suggested a 95 percent certainty that it was Bin Laden. Later, DNA tests comparing samples with relatives found a 99.9 percent match.
Lets assume that there is a 50 percent chance that Mrs. Bin Laden said that the body was her husband's when it was not (error, deliberate misleading, etc.) The facial recognition software said the odds were 20 to one that it was Bin Laden. The DNA match said that the odds were 1000 to one that it was Bin Laden. The estimation procedures would seem to have independent errors (unless Bin Laden had a previously unknown identical twin) so the odds of the person killed in Abbottabad should be of the order of 40,000 to one from this evidence alone. However, the a priori probability of a person hiding in the house in Abbottabad, as the basis for the decision to send in a commando team to attack the house had to be quite high, and that too should have been an independent probability estimate of the three mentioned by the NYT paragraph. I think it is a save bet that Mr. Bin Laden died on Sunday.

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