To summarise, the surface question is whether Christianity was founded by a guy called Jesus who actually walked around and had a few followers who later deified him, or whether Christianity was founded by a bunch of people who believed that Jesus was a god, then wrote a fantasy novel about that god walking around as a human, and later forgot that the novel was only a novel.
The next more fundamental question, and the one at the core of the discussion between the two, is whether Carrier used Bayesian statistics correctly. Finally, underlying all this is the even more general question whether it makes any sense at all to use Bayesian statistics in history, in particular in a quantitative way with actual numbers instead of merely intuitively as a method of organising one's reasoning.
I have written before that I tend towards historicism, then focusing on the observation that quite a few details of the gospels do not make sense to me under the assumption that the authors could freely invent the stories. Somewhat semi-formally one could say that I consider e.g. the probability of the Jesus character being from Nazareth given the hypothesis of the gospels being a novel to be rather low; I would expect a freely invented Jesus to be "Jesus of Bethlehem" because that would more conveniently fulfil a prophecy than the way the authors actually have it fulfilled. On the other hand, I consider the probability of the Jesus character being from Nazareth given the hypothesis of there having been a human who was inconveniently from Nazareth to be rather high.
Reading through Tim Hendrix' critique of Carrier's work and through Carrier's reply, I must admit that I cannot follow every detail, nor can I obviously judge how best to interpret the individual lines from Paul's writings. There are really two main issues that stood out to me, the probability of deification versus historicisation and the derivation of a prior probability from a reference class.
Deification or historicisation
Unless one were to believe that the gospels are completely accurate in their descriptions of every detail of the Jesus story, something that should be impossible even to a faithful Christian in the light of their internal contradictions, it is clear that they contain some material that was made up and some material that at least looks as if it could plausibly be based on actual happenings. For example, even an atheist like myself could assume that a real life doomsday preacher called Jesus did actually in one memorable instance ignore his mother with the justification that his followers were his true family. After his death, however, his followers invented all manner of supernatural stories about him to make him sound more awesome as they tried to convert more people, and thus over the decades he was deified, i.e. raised to god status.
Again, the mythicist idea is the inverse. He started as a god and was subsequently historicised, i.e. his cult started believing that he had really walked the earth although he never did.
The first question here is how probable we should consider either of these options to be, and the second is how probable the gospels would be under either assumption. I must say deification seems like a complete no-brainer to me. It is rather obvious that cultists would have a motive to make supernatural claims or even deify their cult founder, and in fact we have plenty of recent examples of this behaviour. In antiquity this was standard procedure for many important people, especially deceased or sometimes even living rulers.
Carrier argues that historicisation was also extremely frequent: "Hercules, Osiris, Dionysus, Moses, and so on ... were all non-historical yet came to be believed to be historical". I will grant Moses, but I must admit that I remain somewhat skeptical about the others. Surely educated Greeks and Egyptians of Antiquity would have known that Dionysus and Osiris were gods that had some fancy stories attached to themselves? Honestly the idea that anybody would seriously have believed these or Hercules to have existed was entirely new to me when I read this argumentation. And to parallel my observation of recent examples of deification, how often have people in the last few hundred years started believing that characters from novels really existed?
But be that as it may, at best one could conclude that people would have made either mistake with a similar probability. It is further my understanding that the gospels dated to be written first are the ones that depict Jesus as more human, whereas the latest one depicts him the most spiritual. This seems odd under the hypothesis of people slowly forgetting that he was supposed to be merely a spiritual being but fits the hypothesis of people slowing deifying him.
The reference class
Bayesian statistics needs prior probabilities to get off the ground, and this is often one of the strongest concerns of critics of Bayesianism, be it in phylogenetic analysis or elsewhere: how can your priors be justified? It should also be noted that the prior is extremely important, because if it is very high or very low it would require extremely strong additional evidence to push the posterior probability in a different direction. For example, if your prior belief that Columbus reached America in 1492 is very close to 100% certainty, merely showing you a book giving the year as 1489 will not immediately convince you; you may have a moment of doubt but will most likely argue that the book was written by incompetents.
In the case of Jesus, and if I understand the discussion between Hendrix and Carrier correctly, Carrier apparently assigned Jesus to a "reference class" and then used the percentage of people from that reference class who may have been historical as the prior probability of Jesus being historical (c. 6%). The reference class is that of mythical Rank-Raglan heroes. Hendrix criticises this practice for reasons that are a bit too technical for me to fully appreciate, but he also points out that the followers of a human Jesus may well have deliberately assigned him traits to deify him into that class, into the status of Greek cultural heroes and gods. I have a few more problems.
First, does Jesus even fit into that reference class? I must admit that I am highly skeptical in general of this kind of attempt to construct commonalities across different stories. A trope like "comic relief character" is one thing, but "all these stories are basically the same, at least if we ignore all inconvenient differences" is quite another claim. The Rank-Raglan type of hero has a large number of traits, and there does not appear to be a clear cut-off for how many of them a character has to have to be considered sufficiently Rank-Raglan. Subsequently the 22 traits as listed in Wikipedia, with my personal understanding of whether Jesus fits:
- Mother is a royal virgin - Not royal but virgin, so let's say 0.5 points.
- Father is a king - Nope.
- Father often a near relative to mother - Not sure, but I think no?
- Unusual conception - Yes, 1 point.
- Hero reputed to be son of god - Yes, at least in later view, 1 point.
- Attempt to kill hero as an infant, often by father or maternal grandfather - 0.5 for first half of this trait.
- Hero spirited away as a child - Exile in Egypt in at least one gospel, so let's give it 1 point.
- Reared by foster parents in a far country - Far country alone would double-count the previous trait, and no foster parents, so I'd say nope.
- No details of childhood - Non-canonical gospels develop it, so nope.
- Returns or goes to future kingdom - Bit silly, but okay, 1 point.
- Is victor over king, giant, dragon or wild beast - Nope, unless in the most ridiculously figurative sense when he resists the temptation by Satan.
- Marries a princess (often daughter of predecessor) - Nope.
- Becomes king - Again, not really unless interpreted super-figuratively.
- For a time he reigns uneventfully - Nope.
- He prescribes laws - Kinda? He had teachings, so let's give this 1 point.
- Later loses favor with gods or his subjects - Lost favour with Judas I guess, so another 1 pity point.
- Driven from throne and city - Nope.
- Meets with mysterious death - Nope.
- Often at the top of a hill - Yes, 1 point.
- His children, if any, do not succeed him - Not applicable, 0.5 pity points.
- His body is not buried - It is, but then disappears, so 0.5 points.
- Has one or more holy sepulchers or tombs - Trivially applicable to everybody who is venerated after their death, including many historical people, but well, let's say 1 point.
Second, is this not simply circular reasoning? Choosing a class of mythical characters as the reference seems rather convenient. If I were to replicate the analysis, I would be mightily tempted to choose the reference class "cult founder who was deified after their death", eh voilà, 100% prior probability of historicity! And I would not even be able to say how that is any more problematic than the Rank-Raglan choice.
Note that I do not claim professional expertise either in Ancient history or in Bayesian mathematics, merely a long personal interest in history and some professional exposure to Bayesian analysis in a completely different context. I have not even read Carrier's book so far, so clearly what I write should be taken with a bucket of salt. But at the moment Hendrix seems a wee bit more convincing to this non-expert.