What can we call this doctrine? In the old days it was known as probabilism, but this is unwieldy, and it refers to a variety practiced before we really understood what probability was. I think “Bayesianism” is an acceptable alternative, not just because Bayesian updating is the fundamental operation of this system, but because Bayesianism is the branch of probability that believes probabilities are degrees of mental credence and that allows for sensible probabilities of nonrepeated occurrences like “there is a God.”
That’s how I use it. This showed up in Yvain’s response: