Binary chop with uncertain test

[jack]

Suppose I have a sequence of N stages, one of which is anomalous, and I can test one of the stages which tells me if the anomalous stage is before or after that stage. The natural way to isolate the anomalous stage is a binary chop: to test the middle stage, finding out which half is anomalous, and then divide that half into two, etc.

However, if my test is only p=90% accurate, is any other method better? My instinct says "do the same thing, but repeat the test until you're effectively certain". But I always wonder if something else works better.

I'm thinking of debugging. To a mathematician, debugging (or any scientific method) is a MASSIVELY COMPLICATED binary chop. But I always feel like I'm getting the level of certainty wrong. Either I'm not 100% certain I'm testing the right thing and need to go over, or I'm wasting too much time when the problem would have become apparent if I ploughed ahead even if I wasn't sure my test was accurate.

Comments

[jack]

Doh! How did I completely forget that (which looks to be exactly the same...) Thanks for finding it.

[mair_in_grenderich]

had a vague memory of sitting in a canadian cafe while an alsation walked by with a pink teddy bear, scratching in my notebook in pencil. me scratching, not the alsation. that narrowed down the time quite precisely, so i had a look at your posts from that time in case it was one of your problems i was thinking of and turned out it was.

in other ambiguity news i saw this headline "muslims in china fed pork", misread it as "muslims in china-fed pork" and thought the muslims were in the pork. (see also: soylent green). it turned out to be rather less devastating than that, but may have been a consequence of sleepy brain not genuine ambiguity.