Bayesian history research -- some historical hypotheses over time

[lpetrich]

A Test of Bayesian History: Efraim Wallach on Old Testament Studies - Richard Carrier

An interesting article has been published under peer review, which tests my concept (developed and argued in Proving History) that all historical reasoning is already in fact Bayesian (historians just don’t know it), by applying it to the analysis of a major challenge to the consensus that won out in Biblical studies, regarding the origins of the Israelites—the mainstream consensus completely flipping, albeit after decades of debate.

Bayesian representation of a prolonged archaeological debate | SpringerLink

Using Bayes's theorem: P(H if D) = P(D if H) * P(H) / P(D) -- D is some data values and H is some hypothesis. P(H) is the a priori probability of H and P(D) is usually found by adding up P(D if H) * P(H) over all hypotheses H.

One can avoid trying to consider all possible hypotheses by considering ratios: P(H2 if D)/P(H1 if D) = P(D if H2)/P(D(if H2) * P(H2)/P(H1).

Efraim Wallach considered the probability ratios of several hypotheses, and he adjusted those ratios with archeological finds. These hypotheses were:

• Cq: Conquest -- from the Bible (Joshua and Judges)
• Im: Immigration -- peaceful arrival
• Rv: Revolt -- overthrowing previously-dominant group
• At: Autochthonous -- emerging from the already-present population

He started out with P(Cq)/P(Im) = 100, P(Im)/P(Rv) = 100, P(Im)/P(At) = 100, representing what was mainstream in the 1920's. With each find and each major result, he adjusted these values depending on how well it fit one hypothesis or the other. Neutral = 1, of course, anecdotally favoring 1.5, substantially favoring 3.0, and strongly favoring 10.0. So if something strongly favored conquest over immigration, then P(Cq)/P(Im) gets multiplied by 10. Likewise, for favoring immigration over conquest, then the number gets divided by 10.

This may seem like unjustified numerical precision, but the results are not changed very much by tweaking the numbers, and they roughly agree with more subjective estimates of professional consensus.

 

[lpetrich]

The first of these numbers is P(Cq)/P(Im), conquest vs. immigration. It starts off at 100, passes 1 around 1970, and then declines to 0.000004 by 1985. That roughly gets right the time when immigration became more popular than conquest.

As immigration became popular, the revolt hypothesis emerged. Calculating P(Im)/P(Rv), it stayed around 100 until the 1970's, and it then rose to 65610 by 1985. Even making the ratio initially 1 gives a final ratio of 656.1 by 1985. So the revolt hypothesis also faded.

Finally, the autochthony hypothesis. Its ratio P(Im)/P(At) starts off at 100, passes 1 around 1970, and reaches 0.0006 by 1985.

I did something that neither Efraim Wallach nor Richard Carrier did, and I collected these results to find overall probabilities.

Initially, Cq >> Im >> Rv, At, all the way until the 1960's and 1970's, when Im and At catch up to it and pass it. Then At pulls ahead, with Im sinking to less than 0.001, and Cq and Rv sinking to about 10^(-8).


Needless to say, this is very far from the Bible's account of the early history of the Israelites. Richard Carrier:

Wallach notably points out the Bible itself had no real effect. As the historiography of this debate shows it could be interpreted in any way that would support every hypothesis. Certainly there were “experts” who wanted the Bible to be literally true. But there were also experts who wanted to genuinely test what the Bible says against material evidence, and when the two conflicted, the obvious solution was to reinterpret the Bible (as either lying, mythologizing, fictionalizing, fossilizing error, or written nonliterally, among various other ways to make the text fit the facts). This was essentially due to a singular defect of the Bible: nothing in it was written by anyone actually alive when anything it says happened (in the relevant period of time). In fact, all relevant content was composed centuries afterward. By authors with no known skills in critical historiography, no known sources, and an obvious propagandist motivation. That’s literally the worst source to have in the whole field of history.

The dual-monarchy period seems well-supported, because we have plenty of outside evidence for it. In between are the likes of Kings David and Solomon. They likely existed, even if they had not built very big empires.

 

[steve_bank]

From relpability engineering I am familiar with Baysian mrthods/

What it boils down to is given what has been statistically demonstrated and proven in a system, what is the incremental probability of an addition to the sytem?

Given what is proven, what is the probility of an extrapolation based on what you know.

Any historical analysis has to be Baysian in that regard. Given documented history of events, what is the probability of related events not well documented.