Thursday, June 23, 2005

Trouble with Baye's Theorem

Anyone out there who understands Baye's theorem, I'd love some help. I'm just beginning to read up on it, and I can't seem to get it to work for me.

I'm trying to see whether neuroscientific correlations count as evidence for or against dualism. Here's a first try.

So P(h/e&k) = [P(e/h&k) P(h/k)]/P(e/k)

Where:
h= dualism (Thomistic substance dualism)
e1= apparent mental --> physical causation (I also want to try it with e2=physical-->mental causation)
k= background information, like observations of human behavior & experience

It seems that:
P(e1/h&k) would be very high, maybe .8
P(h/k) is at least as likely to be true as false, so =.5
P(e/k) seems very low, maybe = .01 (quite generous in my mind)

But if I plug these values in, I get a probability of 40, which is crazy. Shouldn't it be between 1 and 0? What am I doing wrong?

2 Comments:

Blogger Johnny-Dee said...

Part of your problem is that you are only calculating the probability that the evidence supports your hypothesis. The full-fledged version of Bayes's Theorem is:

P(H|E) = [P(H)xP(E|H)]/[P(H)xP(E|H)+P(~H)xP(E|~H)]

You should check out Ian Hacking's nice little book, An Introduction to Probability and Inductive Knowledge.

10:23 PM  
Blogger chris said...

Thanks, John. I'll check it out. I really appreciate your help.

12:33 AM  

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