That's Kolmogorov's "uninterpreted" probability mentioned earlier in this thread. It's not clear to me yet why uninterpreted probability would be more acceptable to historians than something with an intuitive interpretation that approximates what they believe they are already doing, and approximates what everybody they know (other scholars) believes themselves to be doing, whether in history or in other fields whose adepts wrestle with evidence to estimate truth.I'd like to introduce the notion of probability space, since it allows for consideration of the necessary boundaries required to handle terminus ad quem and a quo issues which are essential to the historical method.
https://en.wikipedia.org/wiki/Probability_space
[FWIW A principled reason for a (non-statistician) scholar to reject Bayes would be to deny that the goal of inquiry is exclusively the estimation of uncertain truth. Some science commentators already do this, citing elegance, usefulness, ..., even outright aesthetics as valid aspects of theory evaluation.
Even a moment's reflection establishes that judging an approximation's merit cannot be exclusively based on its prospects for truth - an approximation can be useful and therefore admissible despite its for-certain falsehood, for example Newton's Laws.
Bayesians would reply that they have "maximize expected subjective utility" models of "value-influenced" decision making. However, it isn't clear that something like the ill-named "Fuzzy logic" mightn't at least sometimes offer a more palatable alternative to Bayesian decision theory for some scholarly applications. Fuzzy has made significant inroads into engineering practice.
Regardless, value-influenced assessment is one pragmatic resolution of the "grue" problem. The "green always" hypothesis has practical value now, in a way that the "grue hypotheses" set "emerald colors have an expiration date of ______" does not. Even if I knew for a fact that some element of the grue set were true, but didn't know which date was true, I might be hard-pressed to find much use for that "improvement" in my knowledge - and meanwhile I don't know that. If I took the problem seriously, then I might class it in with all other "perfect working" inference problems (searchable; the term perfect working, borrowed from reliability engineering, would refer to the situation that so far, no green emerald has been observed to turn blue) and soldier on.]
Statistics: Posted by Paul the Uncertain — Sat Dec 21, 2024 3:04 am