You see the problem. Carroll posits a “God” whose attributes — and the attributes of whose world — can be enumerated in absentia, more or less like a scientific model: We can imagine the model is correct, then make predictions about outcomes. But this isn’t the way most people approach religion. Just as God’s existence can’t be proven through argument (even if many have tried), one can’t very well discount religious experience by reasoning probabilistically that God is unlikely. Experience is the one thing, in the end, that can’t be denied. Much as we might like to imagine ourselves chilly Bayesian rationalists, I suspect that most of us are led to our fundamental beliefs via methods that are much less austere. We go around sniffing the world, rooting through rubble, turning over dirt. After all our searching, many of us find a world that smells like God. Many others (including me) don’t.
Regardless of your convictions, there is a point here that many would-be Bayesians might overlook. Bayes’s theorem allows well-defined models — mathematically well-defined models — to be tested against observations. Now turn that around, and realize that without a well-defined model, Bayes’s theorem is nearly useless. This has important consequences. It means that Carroll’s faith in his probabilistic approach is overblown, like when he says that even though it is “enormously problematic” to apply Bayesian reasoning to the question of God, “we don’t have any choice.” It also means that for those aspects of your worldview that seep subtly into all your observations, math alone probably won’t change your mind.
more here.