So far as I know, the only people to explore the application of Bayes Theorem to historical questions are Jesus mythicist Richard Carrier and Christian apologist WL Craig, who apply it to the same question and get opposite conclusions. This seems like a bad sign going forward.

Bayes Theorem requires something which the historical method cannot provide, that is to say, known quantities. For example, in the classic worked example of Bayes Theorem: 'will Marie's wedding get rained on?', we know that it rains five days a year, and that the weatherman is correct 90% of the time he predicts rain.

We have no such data in history. To take an example, the overwhelming scholarly consensus is that the best explanation for the sequence of events that led to the South seceding in 1861 is that the Southern planter elite wished to protect their very lucrative slave economy.

But how could we put a probability on such a thing? Are historians 100% sure? Maybe 51% sure? Perhaps an in-between figure, 87% (although why should we favor 87 as a percentage over 86 or 88?!). And how do you determine which parameters to use in your attempt to construct the equation?

We can't. Of course, we can put a number how many slaves there were, and how many hundredweight of cotton they picked, and how much their labor was worth in financial terms, but what we can't do is put a number on how important this made slavery in the Southern planter mind.

Both Carrier and Craig are forced to pick parameters and arbitrarily assign probabilities to them. Unsurprisingly, in both cases this leads them to getting the results they want.