We had a large integration test suite. It made calls to an external service, and took ~45 minutes to fully run. Since it needed an exclusive lock on an external account, it could only run a few tests at a time. We started getting random failures, so we were in a tough spot: bisecting didn't work because the failure wasn't consistent, and you couldn't run a single version of a test enough times to verify that a given version definitely did or didn't have the failure in any practical way. I ended up triggering a spread of runs over night, and then used Bayesian statistics to hone in on where the failure was introduced. I felt mighty proud about figuring that out.
Unfortunately, it turns out the tests were more likely to pass at night when the systems were under less strain, so my prior for the failure rate was off and all the math afterwards pointed to the wrong range of commits.
Ultimately, the breakage got worse and I just read through a large number of changes trying to find a likely culprit. After finally finding the change, I went to fix it only to see that the breakage had been fixed by a different team a hour or so before. It turned out to be one of our dependencies turning on a feature by slowly increasing the probability it was used. So when the feature was on it broke our tests.