Johannes wrote:
I haven't been following this thread closely - to my regret, as there have evidently been some very strong contributions - but I wanted to comment on this point:
Analytics wrote:
2- When I look at Bayes' formula, my intuition is that this is in fact the best approach to address this issue. While I agree it isn't perfect, what is better? Is there a better formula that serves as a model for framking an analysis of whether Jesus was a historical figure? Or are you arguing that we shouldn't use any actual statistics when making statements about what the evidence implies about the probability of Jesus existing?
I don't think this is the right question, because it presupposes that Bayes enjoys the status of the theory in possession, so to speak. The question I would wish to pose is
who uses Bayes to resolve any question in ancient history other than this one? I have come across numerous theoretical models for handling ancient texts - Marxist, structuralist, Freudian, deconstructionist, feminist, evolutionary-psychologist and others - but I have never once encountered someone using Rev. Bayes' method as a means of clarifying a disputed point about classical or biblical antiquity.
You could answer this point by saying that the sort of people who are interested in this stuff tend not to be educated in statistical methods, or even numerate. That is certainly so for a lot of us (I can't count to 20 without taking my socks off), but it isn't true across the board. Some ancient historians do make use of quantitative methods. It may, in fact, be that it is advocates of Bayes who are being misled by a preference for the hard, objective-seeming properties of mathematics and numbers.
A couple of points. First, you can implement Bayesian reasoning in an informal way without actually making up numbers and then plugging them into a formula. As EAllusion said, it's just a way of formalizing how proper reasoning with observational evidence happens anyway.
The second part is a bit ironic, though. You can't be a good Bayesian without being a bit of an iconoclast. That's because a Bayesian approach to problem solving isn't very popular in the statistitcs department, either. Most statisticians feel uncofmortable bringing their own
a priori beliefs to the table, and much prefer "letting the data speak for itself." Lead by R.A. Fisher, 100 years ago the "frequentists" beat out the Baesians as the prefered paradigm of mainstream statistics.
However, the Bayesians have the tenancity of pitbulls, and have never conceded the fight. It seems that over the last 15 years we are making some headway within the statistics department, but it is still a minority approach of solving problems. That is why when somebody like Sean Carroll spends 2 chapters in a mainstream book on science preaching that he is a true-beleiver of Bayes' Theorem, it is a big deal.
I wouldn't expect to win this debate in the ancient history department before we've won it in the statistics department. But that doesn't mean we are wrong.