Very nice overview of Bayes Theorem and Historical Jesus

[_Analytics]

The Gospel of Q

What do you think about the theory of a written document Q that the synoptic gospels used as a source (I know, you'll pounce on the word theory). And of course a the theory you're affirming depends on the gospels being late. If Mark and Luke both predate the destruction of Jerusalem, your argument has much less force.

I understand the basic argument: that the relationship between the contents of Mathew, Mark, and Luke indicate that Mathew and Luke were both derived from two sources: Mark and a no-longer-existing “Q”. I’m way out of my depth here, but it seems clear to me that there must be some truth to that. The question that remains is where did the differences come from? Were they just made up? I would think your best case is that the authors of Luke and Mathew really had first or second-hand knowledge of Jesus, but didn’t know where to begin writing their stories, so they (and probably their scribes) sat down with Mark and Q, started copying and compiling, but then made insertions or corrections whenever they had any disagreements or new information.

HI Analytics welcome back,

Thanks, great to be back!

On Richard Carrier, the Prick

Oh yes, I quite agree. I flippantly wrote too generally and should have specified. As I pointed out with a book reference to Philo above I just don't buy Carrier's bias toward the academy that includes atheist, agnostic, jewish and Christian scholars that conclude very unflattering pictures of Jesus to a believer but a mythical Jesus, that could in fact comport better to a believing paradigm, is not taken seriously and the traditional method is somehow abandoned in that narrow undertaking. It is just absurd.

The majority has been wrong before. It might be unlikely that they are wrong, but I wouldn’t call it absurd.

I suppose I’ll also say for the record that I really don’t like Carrier’s views on this being dismissed as a simple “bias” or “strong personal desire for there not to be a historical Jesus” or whatever. He claims that he doesn’t care about the issue one way or the other, and only started down this road because it was a funded project he was asked to do. But regardless, it would be a lot more productive to demonstrate why he’s wrong rather than to just presume that he’s wrong and speculate about what emotional or cognitive shortcomings cause him to be wrong.

"All the Evidence"

More specifically, he's simply claiming that all of the evidence and background information needs to be considered. Then, two questions need to be asked: 1- if the historicity hypothesis is true, what's the probability it would have produced the sum total of all of this evidence? 2- if the mysticism hypothesis is true, what's the probability it would have produced the sum total of all of this evidence? In principle, this doesn't contradict the "traditional historical method", does it?

No not at all, and what you just stated is the traditional historical method. He just doesn't apply all the evidence, which isn't surprising given his lone wolf status.

He endeavors to apply all of the evidence. That’s what he claims in his 700+ page book that painstakingly catalogs the evidence he is considering, at least. He also claims that he would welcome specific additions to the evidence or corrections to how he interprets it or weighs the probabilities.

It does make me wonder, though. Does, say, Bart Ehrman really apply “the traditional historical method” when he sets out to prove Jesus exists. From all of the reviews of Did Jesus Exist that I’ve read, all Ehrman does is make appeals to authority and appeals to the majority, and then list several bits of evidence that allegedly prove Jesus exists. That’s a very different approach than systematically looking at all of the evidence and considering whether it is more consistent with the historical or mystic hypothesis.

Addressing an Actual Issue (THANK YOU!!!)

Symmachus makes an excellent point in regards to this:

Well, it's hardly that simple. That "evidence" doesn't speak for itself and one has to make judgements of some kind about what it is doing and saying in its own context before you can start deciding whether some hypothesis conforms to it or not. There is an interpretive rehearsal that goes on before the show can even begin (see Kish's examples above). We know that the same processes of thinking were at play in thinking about Augustus and about Hercules. How do you account for that in selecting what constitutes "evidence" without already making a judgement that one is historical and one is not?

a good example of what Symmachus eloquently points out in Carrier, and respecting what you found appealing from Doherty is in regards to the silence in Paul. Carrier finds this silence 'bizarre' and since it is bizarre Carrier concludes that it is unexpected, infrequent and therefore historically improbable. (page 515 On The Historical Jesus)

But the wider literature doesn't bear this out. What Carrier finds improbable, and infrequent isn't so, it appears in a large number of other letters, going well into the Second Century, by what are historicist writers. Graham Stanton further points out that this is not just something unique to Christian writings, but that also '[p]recise historical and chronological references are few and far between in the numerous Jewish writings discovered in the caves around the Dead Sea near Qumran'. (Stanton, Graham. The Gospels and Jesus, Second Edition, Oxford Bible Series, 2002, page 144)

The silence of the second century writers is nearly identical to the silence found in Paul….

This is precisely the type of productive criticism that is needed. Thank you. If the universe of evidence that Carrier examines were approached this way and expanded as needed, one could use the Bayesian formula against him; e.g. “So, when the evidence is analyzed correctly and all points are taken into consideration, we see that the probability of Jesus existing is in the 99% to 99.9999% range (rather than the .025% to 33% range that Carrier calculates).

Did Paul Exist?

o here is the question: how do we know Paul wasn't a mystic? It's easy to assume he was talking about the Jesus described in the gospels if you read four gospels before you read his epistles. But if you were familiar with mysticism rather than the gospels, would you just as easily assume he was talking about mysticism? That being the case, what was Paul really talking about?

Well how do I unpack this in a post or a few? How about this, why just ask that question? Plenty of mythicist's outside of Carrier believe Paul himself never existed and give plenty of historical reasoning for doing so. But Carrier has to rely on traditional historians and method for his assertion that Paul was historical. Why wouldn't the traditional method fail here?

The evidence in favor of the existence of Paul is much more clear and direct than the evidence that Jesus existed. We should all be able to agree on that, so that isn’t a very good example to illustrate anything. In any case, Carrier’s point isn’t that the “traditional method” itself fails. His point is that “the traditional method” hasn’t been fully and correctly applied to the specific question of Jesus’s existence.

I’m just not impressed by angry responses to Carrier of the form, “How DARE Carrier question whether Jesus exited! EVERYBODY who is ANYBODY already knows He existed. Carrier’s argument is so heretical I’m not even going to do it the honor of engaging his actual arguments. After all, that’s exactly what Carrier wants!”

That's basically the way Carrier phrases the question. It's conceivable that a historical Jesus was embellished with supernatural abilities and accomplishments. Likewise, it's conceivable that a mystic Jesus was embellished with an earthly history. In light of all of the evidence, which of those two conceivable hypotheses is more likely?

Currently the former. The reasons are manifold.

I’m happy to take your word on it, but it would be helpful if somebody laid out the evidence and demonstrated specifically how Carrier is wrong.

The novelty of a mystic Jesus is intriguing to me. Carrier is a bit of an arrogant prick and I don't particularly like aligning myself with him. But I find his arguments worthy of consideration.

I'm not adverse to using Baye's theorem in the manner you outline for specific and appropriate historical issues and if it helps historical research all the better. I do think your falling for Carrier's smuggling of Baye's to appear more credible but I have deep concerns there as well. My criticism is that Baye's cannot be used properly if its results are so radical from decades and decades of Jesus scholarship from all over the world.

I am yet to read a mathematician or statistician speak highly of Carrier's application and use of Baye's either. If you find one I love to read it….

I happened to shave one’s face this morning, lol.

Carrier Should Stick with History

Respecting Carrier's use of Baye's Luke Barnes who criticised Christian William Lane Craig's historical use of the theorem pretty harshly also blasts Carrier's use of the theorem:
https://letterstonature.wordpress.com/2 ... er-part-1/

Atheist Jeffery Jay Lowder, the co-founder of Internet Infidels reviewed the exchange between Barnes and Carrier he sometimes agrees with Carrier in some points but concludes Barnes' criticisms of Carrier's use of Bayes is a "a prima facie devastating critique". http://www.patheos.com/blogs/secularout ... ne-tuning/
….

I read the Luke Barnes essay you linked to, but I haven’t read, “Neither the Life nor the Universe Appear Intelligently Designed.” From the quotes Barnes provided, it’s clear that in that essay Carrier was being quite sloppy and perhaps inconsistent with his descriptions of different elements of probability and Bayesian analysis. I can’t comment more on what they say without reading Carrier’s actual essay. However, at this point I’d be quite surprised if I found the essay to be very good.

But I fail to see how any of that shows that his general approach in Proving History is invalid.

Qualified Advocacy of Bayesian Historical Analysis
If you are looking for a fully qualified reference that speaks highly of Carrier’s use of Bayes, have you considered Dr. Aviezer Tucker of Harvard University? While not a mathematician or statistician per se, he has written a book published in 2004 by Cambridge University Press called, Our Knowledge of the Past: A Philosophy of Histiography that presents a Bayesian philosophy of histiography.

As Philo noted above, in 2016 Tucker reviewed Carrier’s Proving History in the journal History and Theory. In the review, he confirms that he is still “committed to a Bayesian framework.” He also observes that Carrier “seems to believe” one of my own points I’ve been arguing in this thread: “historians generally practice methods that are derived from Bayesian logic, or at least they should.”

Just think how many one time events happen in history - how is that translated into probability sufficiently? I just see no way out of the subjectivity nightmare with Bayes used in the manner Carrier advocates.

If it’s all too subjective to describe with any real likelihood anyway, how could the “traditional method” make any statement about the likelihood that Jesus existed in history?

[Guest]

I wrote something really cranky, but I'm editing it out.

I guess I will read something on the use of Baye's Theorem on another subject, because, frankly, Carrier's use of Baye's Theorem is simply unconvincing to me. Part of the problem is that I can imagine too many ways in which Jesus seems historically plausible. Unlike the Book of Mormon, which is wildly implausible as an ancient document, because it really does not fit the ancient American context in any way, the New Testament describes a figure who, while a unique combination of traits, fits his historical context remarkably well. Jesus' activities, the response of the Roman government, the actions of Pilate. All of it lines up very well with what we know of the period, how the Roman empire actually worked, the religious politics of ancient Judea, the careers of other religious charismatic leaders in Josephus. As a historian, I read all of those things, and it constitutes a giant checklist of evidences for why Jesus existed.

In Jesus, we don't have a record of a 19th century eskimo showing up in ancient Israel to preach the virtues of seal hunting, only to be executed by Magnum P.I., as translated from Inuit by an illiterate pipe welder who can't produce the original document.

I would be interested in seeing how Baye's Theorem can be used to show me how Pilate did not exist, or that his existence and activities in ancient Judea, which are consistent with his execution of Jesus, in no way support the existence of Jesus. Or how the regular tensions surrounding the Passover, which is an important part of the Passion narrative, do not lend support to that narrative as being historically plausible, or lend credence to the existence of the historical existence of Jesus. I would also be interested to know how the existence of other charismatic religious leaders who do things similar to Jesus--including occupying the temple--show how Jesus is less historically likely.

At some point, I just have a basic issue with people arguing against the likelihood of things that we know are not only likely, but also actually happened and constitute the context in which Jesus' career and execution unfolded. Somehow, Baye's Theorem turns these things, that logically appear to be supporting evidence into evidence against? Altogether insufficient to argue that it is at least more likely that such a historical figure existed rather than not?

I have seen ancient historical narratives with miracle stories and made up speeches about verifiably historical individuals. And yet I am to believe that the same kinds of unbelievable elements in the Gospels obliterate the likelihood of Jesus having existed? If we know these other people existed and were yet implicated into nonsensical tales about divine paternity, healing miracles, and apotheosis, how is it that the same stories about Jesus become proof he did not exist?

[_huckelberry]

Huckleberry:
Philo Sofee , thank you for providing an example to consider, Ascension of Isaiah . I went hunting. Perhaps there are more versions. The one I found was pretty Catholic (it could possibly be read as Docetic as Mikwut noted)
///
". For Beliar was in great wrath against Isaiah by reason of the vision, and because of the exposure wherewith he had exposed Sammael, and because through him the going forth of the Beloved from the seventh heaven had been made known, and His transformation and His descent and the likeness into which He should be transformed (that is) the likeness of man, and the persecution wherewith he should be persecuted, and the torturers wherewith the children of Israel should torture Him, and the coming of His twelve disciples, and the teaching, and that He should before the sabbath be crucified upon the tree, and should be crucified together with wicked men, and that He should be buried in the sepulchre,"

http://www.earlychristianwritings.com/t ... nsion.html

Yes, and none of this happened on earth. That is what makes it so fascinating.

Philo, I just finished reading the whole thing not just the clip. It is a vision of Isaiah which happens in the seven heavens. the incarnation ministry crucifixion burial are all pictured as happening on earth after Jesus makes his descent to earth from the seventh heaven and is born of Mary as a baby.

If you are reading one where the crucifixion and burial happen in the heavens you are reading one completely different than the one I found. Now I just choose the first one to come up by Google.

Yes, as Carrier has noted in "On the Historicity of Jesus," the Ascension is a combination of two or more manuscripts dating from different times, and the earthly aspects were the invented later "pocket Gospel" of a different historical non-original to the early story, spliced into the earlier version of only a heavenly redeemer figure. In other words, it's been meddled with by later Christian historicists stamping their later interpretation onto it, as the scholar Carrier used, Knight, demonstrated. I don't have Knight's books and analysis. At some point I will have to get them. I am simply accepting Carrier is being truthful on this for now.

A number of people on this thread less amateurish than myself in dealing with this subject have pointed out how adding up the number of evidences depends upon a lot of historical analysis wherein different people may see different things. I apprecate the well worded statements of Kishkumen, Symmachus and others underlining the importance of how evidence is evaluated and how that can be manipulated.

This above is a good example. What may appear to me to be gross dishonesty on Carriers part here may well enthusiasm for finding a desire result. Obviously the document is an assembly but I saw no indication of what is suggested by Carrier to be there. As far as I can tell it takes some extensive contemplation, and maybe imagination, to see the excluded elements of a heavenly atonement.

[_Symmachus]

All of it lines up very well with what we know of the period, how the Roman empire actually worked, the religious politics of ancient Judea, the careers of other religious charismatic leaders in Josephus. As a historian, I read all of those things, and it constitutes a giant checklist of evidences for why Jesus existed...I have seen ancient historical narratives with miracle stories and made up speeches about verifiably historical individuals. And yet I am to believe that the same kinds of unbelievable elements obliterate the likelihood of Jesus having existed? If we know these other people existed and were yet implicated into nonsensical tales about divine paternity, healing miracles, and apotheosis, how is it that the same stories about Jesus become proof he did not exist?

Sound of hammer hitting nail on head (followed by sound of Jesus's agonizing screams as said hammer hits said nail's said head).

In Jesus, we don't have a record of a 19th century eskimo showing up in ancient Israel to preach the virtues of seal hunting, only to be executed by Magnum P.I., as translated from Inuit by an illiterate pipe welder who can't produce the original document.

Omfg I can't stop laughing—the best analogy I have ever seen of the problem facing Book of Mormon literalists. Somebody please do a Bayesian analysis to show that the Book of Mormon is more historically probable than Kish's tale told by the illiterate Inuit-translating pipe welder.

[_Kishkumen]

Thank you, consul.

I suspect that those who have come to the realization that their years of belief in Mormonism as a restoration of primitive Christianity supported by genuine ancient scripture were spent in a large measure of historical delusion, then become excited about the possibility that all religion is founded on historical falsehoods and don't know where to stop. This is because, in my view, their overall historical literacy is yet astonishingly poor. I don't hold myself out as vastly superior to these fellow travelers in the struggle against falsehood. I speak as one who, having acquired the smallest understanding of my own ignorance, begins to feel like much more sober study and reflection is necessary before I run to the next conviction.

Is Christianity founded upon historical errors or things that just aren't so? Most likely yes. But the mere existence of a controversial prophet named Jesus, who was executed by Roman authorities, is not one of those shaky elements. I would be the first to concede--as I have done many times in the past--that the evidence for Jesus is far less compelling and confirmatory than most people take for granted, but that is a far cry from saying he almost certainly did not exist.

My feeling is that those who argue for the non-existence of the historical Jesus may be engaging in a salutary exercise, inasmuch as it is always helpful to wrestle with uncertain things to test the possibilities, but are in for some well deserved criticism, particularly when they convince themselves that, despite many solid, albeit indirect, evidences to the contrary, they insist they have demonstrated that there was no Jesus, that instead someone dressed up an imaginary phantom in all of these strongly suggestive supporting evidences for his existence for reasons practically unfathomable.

If the Jewish charismatic religious rebels Judas, Honi, et al. all existed, why should we suppose Jesus did not? Why make up Jesus instead of taking up a real guy when that is so much easier and more likely? In a land full of prophets and doomsayers being hunted down by Roman authorities, someone seriously has to make one up to worship? Isn't it more likely by far that Jesus is an exceptional (in degree) example of what the others are: real religious rebels whose sparsely detailed biographies are shaped by the theological needs of the communities that revere or revile them and accordingly embellished?

Consider the legacy of Simon Bar Kochba. How much do we really know about him? How much of what little we think we know is propagandistic BS or wishful thinking? Are you going to tell me that he was made up too? Maybe Hadrian didn't invade Palestine with his legions and massacre scores of thousands of Jews?

Or maybe Hadrian never had a Bithynian boyfriend named Antinous, who died by drowning during a trip down the Nile, and was then deified by the emperor and became one of the most popular and widespread gods in the empire for a couple of centuries thereafter. After all, we know so little about him. What we do think we know is so stereotypical or mythological. Did not Herakles' boyfriend Hylas get pulled into the water and drowned by nymphs? Did not Osiris die in the Nile and get reborn as a resurrected deity? Maybe Hadrian and his friends just made up Antinous as a form of religious propaganda and control.

Or maybe not. Indeed, probably not. Why should we imagine that Hadrian made up a boyfriend who died in the Nile and whom he deified when we know that Hadrian was a pederast, when contemporary poetry supports the existence of Antinous hunting lions in Libya on the same journey, when the emperor did visit Bithynia, when Egyptians did believe that animals and people who drowned in the Nile became divinities of a sort?

Just how many figures, about whom we have even less data than of Jesus, are we going to strike from the historical record? At what point does it become statistically improbable in the extreme that all of these people were just made up? The problem is the historical fixation on Jesus, and the political footballs associated with belief in him (of various kinds). Precious few people give a crap about Simon, vanishingly fewer about Antinous. This is why Richard Carrier did not do a Bayesian analysis of these guys, and this is why a growing number is so passionately positive about his findings. I am not rejecting Bayesian analysis out of hand (not being savvy of it), but I do believe that a lot more informed thinking about historical probabilities concerning historical figures in general must be done before anyone should begin to be as confident as Carrier's fans are.

[_Symmachus]

I am not rejecting Bayesian analysis out of hand (not being savvy of it), but I do believe that a lot more informed thinking about historical probabilities concerning historical figures in general must be done before anyone should begin to be as confident as Carrier's fans are.

Same here. I don't really see its point yet, but I certainly see the problems in the way it's applied and especially in the conclusions that are drawn from it in this case. I asked above what other historical problems this analysis is being applied to, and I ask that question again here to anyone who knows. It would be interesting to see whether a less controversial problem would yield more rigorous results.

In general I'm distrustful of these things when applied to historical problems for the same reason I'm distrustful of people's blind faith that business leaders will naturally make good governors or presidents. In the current campaign, we have on daily display a hilarious (and terrifying) refutation of that faith, and practical experience over decades has shown that business people are some of the worst executives in government (e.g. Robert McNamara). Running a business and governing are fundamentally different endeavors. But for some reason, in a bizarre secular twist of the prosperity gospel, people are conditioned to believe that if some one got rich in business they are a priori good at everything.

In the same vein, the fabulous technological advances that have come from the application of mathematical reasoning (and of course the fabulous riches!) to certain domains of experience have somehow granted an air of authority to its methods across all domains of knowledge. Carrier is a problematic case because he really should know better (I mean, he really, really should know better, although it's telling that he is more an atheist activist than a historian), but in general when I see these problems treated as if the only thing we need to do is "look at the data" by people who have the only slightest grasp of where the data come from, it's as surreal to me as if an expert whose sole area of expertise were on the late Roman economy were advising the Federal Reserve board on monetary policy. Of course, even though the late Roman economy has almost nothing in common with a modern industrial and technological economy and our way of understanding is not based on mathematical models or sophisticated financial theories and is largely guesswork and deduction from written texts and archaeology—well, even so, if that expert were rich, the board would probably listen with attentive ears. It's a divitiori reasoning, and I think applying Bayesian probability in this way is a variation of that.

[_Kishkumen]

One of the ironies of the cultural obsession with business, which I have referred to many times on this board, is that it was none other than Plato's Socrates, who wisely observed in Classical Athens, millennia ago, that expertise in one area does not amount to mastery in other areas. But somehow we manage to forget that, and we turn to the rich to lead us and solve our problems, forgetting that devotion to wealth is not necessarily accompanied by great wisdom, humanity, or ability to lead others. It definitely means someone knows how to enrich him- or herself. Then we're surprised when that does not work out so well for the rest of us.

But Socrates also taught us that there should be a method of examination that would get at the truth unencumbered by egos and hero worship. Arguably, the application of math to determine probabilities instead of relying on one's gut is partly an outcome of Socrates' own method. So, this may be a little different than the Cult of Business, in that we are talking about a method for determining truth, not a person's ability to make money equaling universal competence. And yet, the faith of the layman, or even the unguarded enthusiasm of an expert, can be very much like the Cult of Business effect. People rely on numbers and those who argue with them in an appeal to authority. If you have pie charts in your presentation, you must be right.

I am pretty confident that Bayesian analysis can tell us that Jesus was not actually all that he is described as in the gospels. And there is a good reason for applying such analysis to these problems. One must be much more careful, however, in determining the fact of his mere existence by the same method. I am optimistic of the possibility that it could work, but I am not sure that we are there yet, and it will take more reflection on the nature of the questions regarding probability involved before we arrive at a more reliable answer. And, I admit that I have far more questions about this than I have answers. What I do have is a broad sense of the complexity of the issue.

[_Symmachus]

Very well put, Kish. I don't mean to dismiss this out of hand—I hope my reasons are at least clear—but I think we should be deeply skeptical of its applicability in cases where value judgements have to be made in setting up the data. As EA said above, garbage in, garbage out. It's the assumption of universal applicability that I reject, and in historical work, as in every other area of intellectual inquiry, it's about the finding the right question to apply these methods. I think the NHM thread is a good case in point: determining the probability that NHM would occur anyway within a given and—most importantly—easily defined set of data is something that I can see as very useful. I mean, it's just a question of adding up inscriptions we do have. There is no value judgement that has to be made in that process. When, however, there are value judgements to be made (e.g. any evidence couched in mythological tropes is less valuable than those that are not so constructed), then it seems to me one is already assuming as true the very thing that needs to demonstrated as true.

To address your point about Socrates, I think it's no accident that a very strident critic of the applicability of Bayesian probability was also one of the most strident critics of Plato (Karl Popper).

[_Philo Sofee]

This has been a truly marvelous discussion you guys. Thank you so much for sharing your ideas and your views. I learned so much from this board. I'm continuing to study the historical Jesus from the historical Jesus Scholars. It is without question one of the very most interesting subjects in all of literature. I hope you won't mind if every now and then I bring up something controversial and argue about it and discuss it. Yes Carriers Bayesian analysis of the historical Jesus is difficult for some people to accept. Until an actual Jesus historian refutes Carriers Bayesian analysis with Bayesian analysis instead of emotion however I think Carrier has done the best job so far. That doesn't mean he's correct I'm not saying that. I'm saying is Bayesian analysis appears to me to be seriously strong. I'm looking forward to the time when someone can show with a Bayesian analysis that all of his background and all of his evidence is probabilistically less than what is in favor of a historical Jesus existed. In the meantime there's plenty of fun stuff to discuss. I love you guys man.

[_Analytics]

Is Christianity founded upon historical errors or things that just aren't so? Most likely yes. But the mere existence of a controversial prophet named Jesus, who was executed by Roman authorities, is not one of those shaky elements.

Carrier claims that given how common Roman executions were and how common the name Jesus was, they probably executed a few prophets named Jesus every year.

Just how many figures, about whom we have even less data than of Jesus, are we going to strike from the historical record? At what point does it become statistically improbable in the extreme that all of these people were just made up....

I think you are seriously imagining that Carrier's argument is something other than what it is. According to Aviezer Tucker, Proving History makes the case for using a Bayesian Analysis, and then shows that argument after argument for the historicity of Jesus are fallacious--a set of "worst practices." He then raises the question of why show a set of alleged "worst practices" to make his point about how history should be done.

He then makes a crucial point:

One of the interesting lessons from the history of science is that to be accepted,
theories and hypotheses do not have to have high posterior probabilities, as long
as there are no competing hypotheses or, if there are, they have an even lower
probability. For example, before Einstein introduced his theory of relativity,
Newtonian theory had low posterior probability because experiments refuted
it, so it required the addition of ad hoc hypotheses or boundary conditions that
dragged down its posterior probability. Yet until a better theory was introduced,
scientists continued to accept it for lack of a better alternative. Accordingly, even
if Carrier can prove that the historicity of Jesus has a low posterior probability, it
may still be rational to uphold it for lack of a more probable alternative. Carrier
does not address systematically in this book the question whether there are better
explanations for the evidence than the historical Jesus hypotheses.

http://onlinelibrary.wiley.com/doi/10.1 ... 10791/epdf

That is a perfect setup for Carrier's second volume. In other words, according to Bayesian Analysis it isn't enough to say there is a little evidence that person X existed in order to claim he probably didn't. Rather, you ALSO need a competing theory that does a better job of explaining the totality of the evidence. That's the difference between using Bayesian Analysis to disprove the existence of Jesus vs. using it to disprove the existence of Antinous. It's not just that there is little direct evidence that both men existed; it's also that there is allegedly a lot of evidence that is better explained by the mysticist theory of Jesus. Until there is a mysticist theory of Antinous that is supported by evidence, Bayesian analysis is going to say sure, he probably existed.