### A Bayesian Spirit Catcher

Since my recent posts on material and spiritual explanations have been so egregiously misunderstood by some commenters, let me try again, with a new tack.

Bayesian inference is given by the rule:

Our H is: "Hildegard of Bingen had visions sent from God."

Our E is that we discover that Hildegard was suffering from migraines. (By the way, this idea is just sheer speculation on the part of Oliver Sacks, with little evidence behind it. But let us imagine it confirmed.)

Let us say someone like my friend Ben Kay has the prior P(H) that Hildegard experienced divine visions of 0. (Ben is a committed atheist.) Then E arrives. Ben touts it as, "See, she just had migraines." But this is insincere: with a P(H) of 0, for any evidence that arrives, Ben will have a P(H | E) of 0!

I have another friend, an Inuit fellow named Nahallak, who thinks Hildegard's life story makes her report of divine visions likely, so that he has a P(H) of .8. But he is also convinced that if someone does have a divine vision, that is certain to affect their body in a profound way! So while P(E) (the probability someone has migraines) may be, say, .2, he also believes that P(E | H) is .2: he was already certain that divine visions have some physiological impact, and so the possibility that someone who experiences divine visions has migraines is simply the probability that they have migraines. So for Nahallak, P(H | E) is .8. The new evidence has no impact, and this is not due to "irrationality," but because Nahallak is a logical Bayesian updater.

To be fair to my critics, there is one class of people for whom this new evidence might result in a P(H | E) different from P(H): if someone thinks visions from God are possible, but, if they occur, the person receiving them will show no physiological response to the vision whatsoever, then P(E | H) will be 0, and the migraine discovery will falsify H. But this is a very odd position, and I have never heard of anyone who holds it. The person in question would have to acknowledge that seeing a tree, or feeling a cold wind, or hearing from one's mother, all produce a physiological response, but receiving a communication from the very source of all being itself leaves the recipient's body completely unmoved!

So, what I have been trying to say is that, except for the very odd position of the last mentioned class of people, E provides no new evidence at all as to whether Hildegard had divine visions or not. If your P(H) was already low, it will remain low, but if it was high, it will remain high, and logically so. And nothing in my argument, anywhere, was about what one's initial P(H) ought to be, so the people arguing about this were completely missing what my posts were about.

And the fact that every person who misunderstood this analysis already had a P(H) at or near 0 is, I think, good Bayesian evidence that I have analyzed this situation correctly!

1. Oyveh.

Your standard in other posts was, was it accepted by the church. So ad arguendo let's go with that.
It's pretty small. Millions of people, few with repeated and church-accepted visions.
Let's be generous and say 1/100,000.

Let's grant P(God) = 1. A crazy estimate but favorable to you. (Would you like it higher?)

P(E) will cancel out out so we needn't estimate it.

So your probability is proportional to 1/100,000. [1/50,000 if p(God) = 2. With Him all things are possible.]

Now let's estimate p(Hilde had migraines). She shows evidence, so it's probably pretty high, but let's stick to
the population estimate, which must be favorable to you.
Here being femail, that is 18%.
Now what about p(Hilde would see stuff|Hilde had migraines). Again let's just use stats. Of those with migraines about 15% see stuff.
Actually it's higher if you count all stuff; I am only counting "aura". Let's use 10%; I feel generous.

p(E|Migraines) is then proportional to 1/50.

SO even using number wildly favorable you your case, the ratios come down on the migraine side, 2000:1 for.
Now toss in mushrooms, toad-licking, starvation, etc.

1. "Your standard in other posts was, was it accepted by the church."

Completely made up. I never offered any such standard.

There rest of your analysis is roughly like this"

Someone claims "Babe Ruth was the greatest home run hitter ever."

Someone else counters with, "But he ate lots of hot dogs!"

I show, quite decisively, that this is IRRELEVANT, and has nothing to do with whether or not he was a great home run hitter.

You come back with an analysis that shows... that eating hot dogs is more likely than being the greatest home run hitter!

2. In fact, I think it is quite possible that EVERY SINGLE PERSON who sees these auras is having a vision from God. but only rare people can recognize it as such.

You keep treating these as mutually exclusive hypotheses, as though EITHER:

1) Gene is hearing Bob Murphy saying "I told you so!"

OR

2) Gene's ear drum is picking up sound waves traveling in the air.

You have offered ZERO evidence that points to (Hildegard had migraines) and (Hildegard had visions) as mutually exclusive hypotheses. And then you want to "factor in" things like mushrooms, which ALSO are not mutually exclusive: someone could be on mushrooms AND having a divine vision. In fact, I personally guarantee the latter possibility can be realized!

3. Now, Ken, you should perform an analysis showing how many, many people have had their ear drums pick up sound waves, versus how very few have had Murphy whisper "I told you so!" in their ear.

2. "someone could be on mushrooms AND having a divine vision. In fact, I personally guarantee the latter possibility can be realized!"

Gene, are you saying that you were high on mushrooms and had a divine vision? Sorry in advance if I'm reading into this wrong.