Quote:
Originally Posted by Jeff Lebowski
Sorry. It's late I guess. Nice job.
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Actually, I think Bayes Rule is very help in this situation. Suppose you think about a person who believes the following:
Let P(A1) = 0.99 (the prior probability homosexual preferences are best understood as a choice. Before he/she read the scientific literature. This probability may come from their upbringing or the hermeneutic that use when they read scripture.)
Let P(A2) = 0.01 (the prior probability that it is not best understood as a choice)
Let P(B|A1) = 0.05 (the probability what we observe the current empirical evidence given A1)
Let P(B|A2) = 0.99 (the probability what we observe the current empirical evidence given A2)
Bayes Rule
P(A1|B) = P(B|A1)*P(A1)/(P(B|A1)*P(A1) + P(B|A2)P(A2))
P(A1|B) = 0.05*0.99/(0.05*0.99 + 0.99*0.01) = 0.83
Nice result! Their prior was so sharp that the posterior probability didn't move much despite the overwhemingly evidence. They still believe there is an 83% chance that it is best understood as a choice. I believe this answers MW earlier question (assuming no math mistakes).
In fact this is the source of much message board conversation in general. People with sharp priors and people with more diffuse priors arguing endless because they come to vastly different conclusion about the implications of the data. Bayes rule is wonderful.