I see two major issues with respect to the Bayesian analysis of Resurrection history. One has to do with the left side of the theorem. Is there some way of showing that everyone ought to go into the discussion with such a low prior for any miracle that we can virtually guarantee that nothing coming out of the ancient world will be sufficient evidence.
The usual approach to getting that result is via some form of frequentism. There have been 96,100,000,000 persons who have ever lived, there has only been a very few resurrection reports that have so much as surface credibility, so therefore the one in 96.1 billion, and therefore resurrection has to lose even to the swoon theory. But these lead-footed methods don't work for various reasons that have been pointed out quite often. Earman is, I think, the guy you have to get around if you think you can prove something like this about the prior for miracles.
If you say "Extraordinary claims require extraordinary evidence," (which invariably implies evidence that you're never going to be able to get out of the ancient world), then you have to figure out how do define extraordinary in this context. Does it mean historically unique? In that case you have Indian Prince worries, and there's even a problem believing media reports that Obama won the election. If you think it means contrary to the laws of nature, then why do you presume that every event has a natural cause? Doesn't that beg the question from the beginning? Whether a miracle-working God exists is part of what's at issue here. The skeptic needs an account of extraordinariness that doesn't beg the question and pins an unmanageable prior on all miracle claims for everyone.
The other issue looks at the right side of the theorem, and asks if the evidence surrounding the resurrection is more like what we should expect if the miracle happened or more like what we should expect if it didn't happen. My approach on this is to say that prior probabilities on the matter are certainly going to vary, and that nevertheless we can see if the evidence confirms the miracle story of disconfirms it. Unless you have an argument that shows that no one should have a manageable prior for miracles, you can and should ask this question.
Now notice that I have nowhere said that there is some definite conclusion that everyone will come to, that it is 94% likely that the Resurrection happened based on historical evidence. I am interested in whether the case for the Resurrection confirms it, even if many unbelievers fail to find such evidence "extraordinary" enough.