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Comment by Ukv | Hacker News Reader

> Pangram boasts a false positive rate of 1 in a 10,000. That is, if Pangram says a block of text is AI there is only a one in ten thousand chance that it was written by a human.

That'd be if they had a false discovery rate of 1/10,000.

If for instance:

* 100,000 samples are tested

* 100 of which are AI-generated, the rest human-written

* Pangram flags 50 of the AI-generated samples (true positives)

* Pangram also flags 10 human-written samples (false positives)

Then the FPR is 1 in 10,000, but the chance that a flagged sample isn't actually AI (FDR) is 1 in 6.

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Populare Science is built on a foundation of misunderstanding p-value.

https://www.graphpad.com/guides/prism/latest/statistics/comm...

(OP isn't exactly talkigh about p-value, because it's not comparing means, but the main mathematical structure of the Bayesian error is the same)

Of course, it's unclear if the article is using the wrong term, or the wrong definition, or if Pangram is just lying in the first place.

The classic. If there is one concept people should learn from stats it should be base rates and the Bayes update. It's very difficult to teach though. The mind just jumps to that interpretation, and even if you teach it, people just go right back to interpreting it like that anyway, because they think "yeah yeah technically something something math, I know, but basically in practice it kinda just means that anyway". Even plenty of educated professionals in science do not understand this and continue to get it wrong each day.

In your scenario,

  False negatives = 50
  False negative rate = FN / (TP + FN) = 50 / (50 + 50) = 50%

Their actual FNR is much better than 50%, more like 1% at worst.

It's virtually impossible to have both a false positive and false negative rate of 1% for any predictive model. This is inherently a tradeoff. In addition to the terrific parent comment, you can trivially push false positive rate to 0% by never predicting a positive outcome or push false negative rate to 0% by always predicting a positive outcome. Finding the sweet spot somewhere in the middle is what we try to do, and generally for criminal investigations, which is probably what this is closest to, we err on the side of false positives at the cost of more false negatives. We'd rather let the guilty go free than jail or execute the innocent. There is an asymmetric cost to the different types of errors.

But as the parent says, this means you're still making plenty of mistakes. You're just not making the specific kind of mistake you're trying hard not to make, though I'm pretty skeptical of anyone claiming 1% false positives. It's hard to even envision a truly valid way of assessing this. You'd at minimum need an adversarial test set created by an independent third party that has no incentive to be favorable to you, and even then, the landscape is so constantly shifting that an error rate estimated at one time tells you not exactly nothing about a future time, but this isn't exactly estimating the strength of gravity. You can be correct one week and wrong the next.

Not a statistical estimate, but getting shot in the head doesn't even have a 99% kill rate.

See for yourself: https://www.pangram.com/research/model-card/pangram-3-3

They are advertising FPR<1% and FNR<1%

I'm just as skeptical as you. They mention methodology but it's pretty light.

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