I'll start off by reposting what I wrote after glancing over the paper in another thread:

I might take a whack at it when I get to a computer, because statistics do have a use in economic studies so I am somewhat familiar with the methodology. As far as I can tell, the problem is firstly, that he seems to ignore that historians don't just gather data, do History to them, and thus create facts. We, or at least most of us, are not nineteenth century Germans anymore.

Secondly and far more seriously, he seems to misunderstand the nature of historical data. Historical data is not like empirical scientific data because we do not observe History and record results. Rather, we weed through a mess of second hand accounts, gossip and proxies and try to sort through them. The way we sort them can then be contested--imagine if every chemistry experiment ended with a result that one person could say is lead, but another could say is tin. This is actually a really bizarre misunderstanding for a classicist to have, because our source material is so problematic.

Statistics can be very useful, in my field scholars like Scheidel and Morris regularly produce fascinating, provocative material using statistical analysis. But they use this analysis as a trail marker, not a conclusion in and of itself. Getting a statistical result is the first step, not the last.

Or at least that is my take after glancing over the paper. Really, it all seems like a way to give pseudo-scientific blessing to one man's Quixotic quest to prove Jesus is a lie.

After giving the paper a more full read, I see that what he is claiming is not what I thought it was, and so I need to add a bit too it. Essentially, the way this method is going is either going to end at an absurd overreach, if he decides to take a statistical approach and actually quantify the probabilities of various historical nuggets, or absurdly trivial, if he doesn't. I'm assuming it will be the latter. In essence, what he is doing is crafting an elaborate fistful of sand to throw in his opponents' face and try to confuse the issue. What he seems to intend to do is break up every individual statement and analyze them individually, which may be attractive from a logical perspective but is terrible historical methodology. Not every field can have the same standards of logical rigor as something like mathematics or formal logic because not ever field is using the same sets of data or attempting to reach the same conclusions. This isn't to say that historians do not look at minute details, but they do so in the knowledge that minute details are not very useful in and of themselves, what matters is the argument constructed from them. Historical research is like building an elaborate building--no individual brick or pillar is very useful or strong in and of itself, it is how they are put together.

As I said before, he is a classical scholar and should thus understand this very well, as our source material is pretty awful by many standards. It is too rigorous for the aims of the discipline and its material. Imagine if, say, a biologist was unwilling to rule on the process of evolution unless he had demonstrated its existence to the level of evidence an rigor required by, say, structural engineering or experimental chemistry. You would quickly conclude that no, we cannot rule on the existence of evolution, which I think you will agree is a less correct and useful answer than one obtained by less rigorous methodology.

He must know this, and therefor I can only assume that he continues to use the highly subjective terms as to the level of probability of any given piece of data. He is essentially thus doing nothing to actually advance the analysis of sources than adding a pseudo-scientific sheen to it. I further assume that most people within the historical community will notice this immediately and ignore it, but those outside of it may be taken in by what is, essentially rhetoric.

The long and skinny is that this adds nothing, but appears to and is thus, possibly unintentionally, incredibly deceptive.

I should note that as I am somewhat familiar with Carrier's arguments are broader goals, and am not sympathetic to them, my analysis of his methods is based to an extent on my knowledge of what his conclusions will be. If you want a clarification, or want to dispute something, I'll be happy to try.

I guess I should try to give more detail.

Bayes's Theorem is a mathematical statement which, roughly speaking, describes a process of learning.

You have a hypothesis ("Caesar really did cross Rubicon and started a civil war", for example), then you look at evidence (works of Plutarch, for example), and then you judge that your hypothesis became somewhat more likely.

Three pieces of information are necessary for usage of Bayes's Theorem:

1. how strongly would you expect to see such evidence, assuming your hypothesis is true (in this case, very strongly, as it would be very strange that a trustworthy historian would fail to mention such a significant event). This is a Prob(E|H);

2. how strongly would you expect to see such evidence, assuming your hypothesis is false (in this case, the only explanation would be that Plutarch is lying or mistaken, which isn't very likely). This is a Prob(E|not H);

3. how likely your hypothesis per se, without any considerations involving evidence in question (how often were civil wars in Ancient Rome?). This is a Prob(H);

The exact formula of Bayes's Theorem is irrelevant for our purposes; we can treat it like a black box which takes three numbers and ouputs a single number, Prob(H|E), which meaning is "how strongly we are warranted to believe in H, given what we claim we know".

Any good argument about what is likely and what is not, should be aware of all three things, explicitly or implicitly (you can find a formal proof of that claim in a first chapter of Probability Theory: Logic of Science by Jaynes).

Bad arguments miss something; for example if I claim that Jack the Ripper was an alien, and there is some fact which fits "Jack is alien" very well, and nothing else can explain it so well, then my belief is still not justified, because my hypothesis was very improbable a priori. I have big P(E|H), small P(E|not H), but it doesn't matter because P(H) is neglible, one piece of evidence is not enough to outweigh this.

Very bad arguments have nothing to do with P(E|H), P(E|not H) and P(H) at all.

Having said it all, it seems convincing that usage of Bayes's Theorem is desirable, as it makes explicit all our assumptions and errors. Also, it easier to argue because you can see that the cause of your disagrement is (for example) that you think that P(E|not H) is low, and opponent thinks that it is high.

However, it is far from obvious that we are actually able to estimate all relevant quantities outside of toy examples. Humans don't think in numbers (and those who do tend to become mathematicans instead of historians).

And Carrier proposes a method which (in my understanding) solves this problem, at least in principle (basically, he proposes using rough reasonable estimates while being aware that those estimates are rough). But nobody seems to be aware of it; hence my question.

I hope I managed to describe a general picture of "why?"; if not, feel free to ask anything.