If you have no way of knowing whether the sun has exploded in the last eight minutes, yes. If you have some conclusive reason to believe that, then it's not faith, it's an educated guess.
Given just about any observation could be used to either support the existence or non-existence of God, there's no way to achieve conclusive reasoning on the subject, which means any belief you have on the subject is based on faith, whether it's faith in X religious principle or faith in X scientific/mathematic principle.
As far as I can tell, Bayesian inference doesn't help one way or the other on this subject. It may, however, provide more credence to the theory that, if he exists, God is a dick given the prevalence of shitty things he permits to take place in his name, but that wouldn't do anything toward proving or disproving his existence in the first place so it doesn't really help. (Alternatively: that he doesn't have power to affect human actions, but that would probably conflict with most religions' interpretations of deities.)