As I said in a comment, I'm reading a book today, Why God Won't Go Away, by two neurologists who have shown that mystical states can be shown to be empirically real, and are like states involving the genuine perception of real things, and not at all like delusion or brain disease.
There are some sceptics whom, I believe, might be swayed by this -- as these neurologists were. But most will simply ignore it. Their resistance to any evidence on this issue is sometimes astonishing. Often, I feel I'm in a dialogue like the following. (The house and man metaphor aren't meant to be anything too profound -- I just happened to be looking at the path to my neighbors house as I was writing this.)
"There's a nice chap in the house at the end of that path through the woods."
"There's no house there, and there's certainly no chap!"
"No, I was just there -- there is a house, and a man lives in it."
"That's just a childish fantasy."
"Well, go down the path and look for yourself."
"It's a waste of time -- there's nothing there!"
Of course, if no one else could walk the path and find the house and the man, there would be a good reason for me to start to suspect I'm a little off my rocker. But when I discover that thousands and thousands of other people have walked down the path, seen the house and the man, and described them in similar terms as me, and that those people otherwise seemed sane and intelligent, then the evidence is overwhelming: there is a house and a man down the path, it can be confirmed empirically, and atheists -- you just haven't gone down the path. If you're just not interested, or are still sceptical, fine -- we can still be friends. But isn't it a little arrogant to confidently declare to me that to "believe" in the house and man is nuts? ("Believe" is in quotes because I "believe" in God in the same way I "believe" in the tree outside my window.