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Yglesias

Bacterial Fingerprints and Bayes’ Law

File-EscherichiaColi_NIAID

Lindsay Beyerstein describes a potential new tool for criminal investigators, “traces of bacterial DNA [that] can be used to link people to objects they’ve touched.”

The technology isn’t ready for prime time yet. So far, the method has only proved 70% to 90% accurate. Much more testing will have to be done before this kind of evidence gets anywhere near a courtroom.

I certainly hope more testing is done, because this seems like a technology that comes fully loaded with the possibility of serious mathematical errors. For example, suppose I find a dead body, a murder weapon, and on the weapon traces of bacterial DNA. Then I pluck a random person off the streets of Washington DC and the bacteria on his finger matches according to a test that’s 90 percent reliable.

A lot of people are going to read that as indicating that there’s a 90 percent chance that the random person is a murderer.

In reality, there are about 600,000 people in Washington DC and if you submitted them all to a 90 percent accurate bacterial DNA analysis, you’d wind up with 60,000 false positives. And since there’s only one gunman, the odds that your random person is the killer aren’t 9 in 10, they’re 1 in 60,000—the guy is almost certainly innocent. And improving the test to 99 percent accuracy doesn’t help much. But people make this mistake all the time, whether it comes to “data mining” to find terrorists or giving mammograms to young women with no risk factors. Even tests that are fairly reliable in a statistical sense need to be used very carefully.

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