I was doing some research on Bayes Theory and how it correlates to the resurrection of Jesus. Dr. Richard Swinburne calculated it at 97%! This calculation left some atheists and non-Christians baffled (for instance, Dr. Bart Ehrman refused to deal with Bayes Theory in Dr. William Lane Craig's rebuttal), but Michael Martin took a stab at Bayes Theory and concluded the opposite, that the probability of the resurrection happening is below 50%!* How do you see Bayes Theory and the probability of the resurrection? is Dr. Martin right about his calculations?
-Eddie

First, it is important that we restate what Bayes' Theorem actually is for the sake of other readers who may be unfamiliar with it:

For our present purposes, P(B|A) refers to the conditional probability of the specific evidence obtaining (B) given the resurrection hypothesis (A).  This is then multiplied by the prior probability of the resurrection hypothesis (its mere likelihood given what we know about the world).  It's then divided by itself plus the probability of some alternative explanation to the resurrection (P(B|Ac)P(Ac)).

Now, I haven't seen Martin's interaction with Bayes' Theorem, but the interchanges you described show precisely why historians simply do not use it in assessing historical explanations. Professor D. Matthews writes:

"It is mathematically demonstrable that these prior probabilities will be 'washed out' with repeated use of Bayes formula, however problems arise due to the fact that there can be no reliable way of determining the posterior probabilities necessary to wash them out" ("Epistemic Humility: A View from the Philosophy of Science", Wisdom, Knowledge, and Management: A Critique and Analysis of Churchman's Systems Approach, Vol. 2, edited by J.P. van Gigch and J.J. McIntyre-Mills, Springer, 2006, p. 110).

The reason for this is not surprising.  Each proponent of the resurrection (and detractor) will assign a different value to various variables within the calculus. The overall point that needs to be emphasized is that we cannot assess the probability of the resurrection solely on the basis of whether miracles are likely or not (one can even assign a modest .00000001 to the probability of the resurrection given background information only). Rather, that probability must also be multiplied by the likelihood of the specific historical evidence involved entailing the resurrection hypothesis and against the probability of some rival explanation. When taken in concert, the addition of no competing explanation being likely and the strength of the resurrection hypothesis entailing the specific evidence force the equation's result toward 1 (which is "certainty"). Minimally, the equation need only proffer a value higher than .5 in order to command some assent to the resurrection. Given the alternative explanations, their deficits, and the strength of the resurrection as an explanation, I'm inclinded to say that the resurrection hypothesis enjoys considerable support and is highly probable as a historical event.

Recommended reading: