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Thank you, this is really interesting. I am quite often using the similar "one-way confidence bands" in my own professional work, when using sample date when all the sample observations either show a "Yes" or "No"
The "rule of three" introduced at the end could be very helpful for us. Do you have any links to papers or books where this is explained more in detail?

Magnus: Wikipedia has a page on Rule of Three. It literally is the calculation I did above. The only thing is it applies a standard approximation for the log function to simplify the formula. This "zero events" problem has been studied by statisticians a lot - that's because it's a special case where classical statistics lead to an absurd answer.

There are two typos: in the following sentence 30 sould be 300:
The chance of 300 negatives in 300 samples is (0.99)^30 = 5%.
Even in the next one.

AR: Thanks for spotting them. Fixed. Yes they should be 300 not 30 in those two formulas. The cutoff for 5% was correctly stated at 99% specificity.

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