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False positives at NSA

Do the numbers behind Prism add up?
by Carl Bialik, Numbers Guy blog, Wall Street Journal, 14 June 2013

We are quite familiar with the false positive paradox in diagnostic medical testing: in wide-scale testing of a low risk population, a substantial proportion of the positive test results may turn out to be false. In recent Chance News items have discussed mammograms to screen for breast cancer, PSA test for prostate cancer.

This Numbers Guy column addresses the risk of false positives in the NSA's Prism initiative that tracks electronic communications. Bialik cites analysis by Cory Chivers, a grad student at McGill University. Applying Bayes Theorem, Chivers find that there is only a 1-in-10,000 chance that message flagged by Prism would represent a real threat.

Discussion
1. The article quotes University of Massachusetts statistician Michael Lavine as saying that Chiver's analysis "makes simplistic assumptions that might not pertain to the actual PRISM program." Read Chivers blog post. What assumptions underly his analysis?

2. David Johnson of the Center for Advanced Studies in Washington is quoted:

Submitted by Bill Peterson, based on a suggestion from Margaret Cibes