Friday, April 20, 2007

profiling shooter? you can't profile school shooters

One of the problems, they say, is : There are far too many people who are depressed and lonely are not mass-murderers. And how ever finely you make up a profile, the number of false-positives* will be more than true mass-murderers that fit that profile. This reminds of the Bayesian estimation "paradox" that Arunn on Nanoscience posted a while back.
Example: False positive in a medical test (example taken from [1])

A “false positive” in medical terminology is a situation when ... a person not actually having a particular disease or conditions may be returned a positive result in a test. ... Suppose that a test for a disease generates the following results.

(1) If a tested patient has the disease, the test returns a positive result 98% of the time, or with probability 0.99
(2) If a tested patient does not have the disease, the test returns a negative result 96% of the time, or with probability 0.96.

Suppose also that only 0.1% of the population has that disease, so that a randomly selected patient has a 0.001 prior probability of having the disease. The question now is what is the probability that a positive test results in a false positive?

from back of the envelope calculations:

If there are 1000 people, 1 person has the disease. of the 999 people only 96% were detected. so 39.96 were detected positive, but don’t have the disease. So only 1 in 40 people detected to have the disease really do have the disease.

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