One Bayesian style argument for atheism I run across on the internet goes like this:
The more specific the claim, the lower the intrinsic probability. Atheism is merely nonbelief in God or gods. That's simpler, less specific than theism, much less Christian theism in particular.
Seems to me there are two basic problems with that strategy:
i) It artificially isolates atheism, as a bare proposition, from godless reality. But don't we need to compare one state of affairs with another state of affairs?
What's the overall complexity of reality without God compared to reality with God? Is reality with God a more specific claim? Is reality without God a simpler claim?
ii) What about the proposition that before God made the world, only God existed. Is that claim more specific or less specific than naturalism?
There's also the ambiguity of complex with respect to what. For instance, take decorated pottery. That's more complex than unadorned pottery. But would it be sensible to say that the existence of decorated poetry has less intrinsic probability than merely utilitarian pottery?
Poetry is more complex than prose. Likewise, there are novelists who revel in complexity, viz. Umberto Eco, Italo Calvino, James Joyce.
By the same token, composers like Bach revel in complexity.
That's a facet of human creativity which mirrors divine creativity.
As a friend of mind observes:
That entire approach is foolish because it acts as if we are in a pre-evidential state--a state with no evidence on the subject. The non-existence of my mother is also "simpler" than her existence with respect to a situation where I have no evidence, but, y'know, I have plenty of reason to believe that my mother exists! It would be much less simple to try to explain away the evidence for my mother's existence while denying her existence. That would require a more complex hypothesis than the hypothesis of her existence (e.g., someone pretending to be my mother who isn't really my mother, my having come into existence somehow without a mother, etc.).
The non-existence of anything can be regarded as simpler than the existence of anything, but that doesn't mean the most rational position is the belief that nothing exists! Entities should not be multiplied without necessity, but we are constantly confronted with the evidential necessity of postulating entities, from atoms to zebras, from other minds to God.