Bayesianism is a mathematical concept, but it is used in epistemological contexts. Basically, it is a model of what confirmation is.
From the Stanford encyclopedia of philosophy;
Though a mathematical triviality, the Theorem's central insight — that a hypothesis is supported by any body of data it renders probable — lies at the heart of all subjectivist approaches to epistemology, statistics, and inductive logic.
My overall picture of epistemological justification goes something like this. We all start from different places, and have different initial dispositions with respect to the world as we experience it. Then, we acquire further information. Historically people have tried to pull their model of the world apart and start only from certain basics, and believe only what can be built up from there, but I don't think that's necessary, especially when the people who say we have to do it disagree about what has to be in the base. I think it makes more sense to adjust the beliefs we have as we go along and move incrementally toward consensus as evidence comes in. And with some things, the hope of consensus is pretty slight in the foreseeable future, so we are going to keep disagreeing. I think, for example, that atheists and theists are here to stay for a long time, and the fact that we aren't closing in on agreement does not necessarily mean that one side or the other is just being stubborn or delusional. I would say it's because the issue is too complex and there are too many parameters to it to be sure that we have considered everything, and fairly. It's easy to come up with motives for our opponents, but that in itself proves nothing whatsoever.
I believe in God, but there is plenty of disconfirming evidence. It is just that the confirming evidence, all told, outweighs it, as I see it.