psychology is magic.
I have been following missionary activity in the 10/40 corridor for a little while now and have read and heard about miraculous events in peoples lives. I believe these reports because I know some of the people making them. The head of Gospel for Asia has spoken at my church and is well respected by his peers. He is not a "crack pot" and has no reason to not report what's going on accurately.
Also, we have had former muslims testify at church about an "inner call to Christ" before they ever met a Christian or heard The Gospel.
In the west we can't conceive of these things because we are raised to believe everything has a scientific explanation, but that doesn't make it so. All this conditioning does is make us less likely to see the miracles that occur right in front of us.