I've done extensive study of religions and various belief systems and come to a conclusion. You can stack cognitive bias to the point you perceive things that aren't there. It's actually fairly simple. Belief acts like a filter for reality, we know that much. The thing is you can absolutely stack the effect. Faith in the power of faith, something central to the christian religion can produce those results. Faith in the power of faith is like a loop that throws off your perception of reality enough that you see or feel God or angels or demons.

I'll try to draw a diagram.

Belief ---> Skewed Perception ---> Evidence (repeat)