Date: Feb 18, 2013 9:07 PM
Subject: Re: Trying to understand Bayes and Hypothesis
You cannot escape the subjectivity built into Bayesian statistics.
If you were modeling over the set of all known computable distributions, even the weirder ones that you do not really believe are likely, you are still constraining the set. What about the undiscovered distributions?
Let S1=the Poisson distribution
Let S2=the Normal distribution
Let S3 be the set of all possible valid distributions less the Poisson and the Normal
You can calculate the Bayes factor between S1 and S2 because you can give them mathematical form for a set of observations. You have to be very careful when you fail to use complementary hypothesis and Bayes factors as the meaning is only "Given the data, S1 is a better/worse/indifferent fit to the data when compared to S2"
If they were complementary hypothesis you could say S1 is in the credible set of hypothesis and S2 is not.
In the former case, you can only speak of relative fit. In the latter case you can speak of absolute fit.