Good point Vladimir. What phrase would I use to convey not just having too little evidence but having evidence that just happens to be concentrated in a really inconvenient way. Perhaps I'll just go with 'bad priors'. Such as the sort of prior distribution you would have when you had just drawn three red balls out of a jar without replacement, know that the five balls left are red or blue but have no clue that you've just drawn the only three reds. Not so much lacking evidence but having evidence that is bad/pathological/improbable/bad/inconvenient.