Bayesian equivalent of 5-sigma

With Winston Harris (MTSU) I am working on automating some aspects of discovery and decision-making in exoplanet science. Today we discussed the Bayesian and frequentist equivalents or analogs for a 5-sigma detection or measurement. It turns out that there are quite a few different ways you can define this. Some of the different ideas can be made to collapse to the same thing when the likelihood is Gaussian (in parameter space), but of course the likelihood is rarely precisely Gaussian! So we have choices to make. And of course when I say "5-sigma" I mean whatever threshold you want; it doesn't have to be precisely 5-sigma! A key idea that will guide our choieces is that Bayesian priors are measures with which we do integrals. That said, we will also make principled frequentist methods too. It's not obvious that you want to be Bayesian when you are claiming a discovery!