Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief
Suppose I just don't know the probability of something, having considered everything else, and so would then place its likelihood at 50%. But also suppose I can nevertheless justify the claim that the best explanation for it is mistaken. Can I then conclude that the likelihood of either is less than 50% (and does anyone say that <50% mean it =0%: if I really have considered every other argument?)?
An explanation is a story about what caused an object to exist, or an event to occur.
I think perhaps Bayesian theory says yes, at least supposing we can talk about the probability of an explanation that does not really explain (because what it explains is likely not the case, or for some other reason). Quoting from the comments (emphasis added):
You have the prior p(G)=1/2, and you are asking, I think, about the posterior p(G|B'), where B' is that Bible is historically inaccurate? If you can justify that P(B' | G)
... i.e. that God's existence reduces the probability that the Bible is historically inaccurate, then your posterior does have to be less than your prior, since p(G|B')=P(B' | G)/P(B')p(G) by the Bayes's formula.
Does the answer change if I have to "make a bet", because whatever I decide has practical implications?
A simple argument from analogy is that if my cheating at dice is the best explanation for my winning then my not cheating at dice implies I won't win, and my not winning implies I am not cheating at dice.
Here are two more convoluted examples of arguments on this basis: I'm only interested in the inference in bold. In the first the best explanation is not valid; in the second the best explanation is not sound.
A. The best explanation of my death is that everyone will eventually.
B. In fact, that explanation fails (Heidegger).
C. So the likelihood of my death decreases.
D. There can be no scientific argument for my death.
E. So I cannot die.
The best explanation of the bible's historical accuracy is that God exists
In fact, the bible is not historically accurate.
So the likelihood of God existing decreases.
The best explanation of the Bible being an argument against God is that all revelation and miracles are bunk.
So all revelation and miracles are bunk.
There are no sound a priori arguments.
So there is no God.