By "similar statement" I meant a statement about how often the method will lead you to the incorrect conclusion. If you can't quantify that, it seems to me you don't have any basis for claiming your method "works".
If that is what you meant, than you are getting in the realm of hypothesis testing. The best equivalent of a p-value is then an anabashedly named "Bayes factor" [1], which is a ratio of posterior probabilities for competing hypotheses.