This really only helps with the existence of miracles in general, not specific miracles (there's very seldom going to be enough witnesses of a single event). But all the probabilities are completely arbitrary, you can't make measurements to get the "real" values or even an estimation of a real value, unless you have some "known miracles" first. P(miracle) is unknown, so is P(witness claims miracle|miracle), so is P(witness claims miracle|~miracle).

The only thing we can assume is P(witness claims miracle|miracle) > P(witness claims miracle|~miracle). But even that works only under the assumption that people can somewhat tell what is a miracle and what isn't.

I'm not sure I like trying to do statistics with rare events triggered by a specific person (God), not some natural process.

@kutschkem Yes, "the probabilities are completely arbitrary" is more or less my point; the method doesn't really serve except to reinforce one's a priori belief. That said, with respect to "the existence of miracles in general", if the existence of the supernatural is established, that must surely affect those prior probabilities.

That is, someone who believes in materialism is going to ascribe a very low value to P(M), whereas I would argue that P(M) should be much more likely if materialism has been falsified.

Similarly, consider my discussion with lupe, who has a strong personal motivation to reject God. Lupe is going to be predisposed to assign lower weight to evidence which seems to support P(God) and higher weight to evidence which supports P(~God), whereas, being a Christian, I do the opposite. We both have the same evidence, but come to opposing conclusions.