BaseRateFallacy

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Suppose you have an iris scanner that has a false positive rate of 10% and a false negative rate of 10%. Suppose you know that at most around 1 in every 1000 people you scan will be trying to pass themselves off as someone they aren't.

Suppose you've just scanned someone and the scanner says they aren't who they say they are. What are the chances that that's true?

wrong: "The false negative rate is 10%. This means for every hundred people whose scans don't match their identity, 10 will be false negatives and 90 will be forgers. So the probability that I've just caught a forger is 90%."

right: "In every 1000 people I scan, there will be, on average, one identity forger. Also, 1 in 10 of the remaining 999 people scanned will be thrown up as identity forgers - that makes 99.9 people. So the odds that I've caught a real forger are 1/100.9, or a little under 1%."

What about the more realistic situation where you don't know the rate of fraudsters, as if you're given that bit of information it obviously makes things a lot easier?

: You can safely assume it'll be much lower than 10%, IMO.

I thought the whole point of this page was that it was dangerous to 'assume' anything about such statistics.

: Nope. Wasn't. :P

Why should I assume that?

: You don't have to. MoonShadow has no wish whatsoever to foist his weird religious beliefs upon anyone else ^^;

Did PeterTaylor correctly correct MoonShadow's example? Comments..?

MoonShadow did wonder about that, but wasn't sure quite how to go about iris-scanning .9 of a person ;)

: PeterTaylor wonders whether it would be in bad taste to observe that provided they have an iris...