September 2005 (UTC)

One of the great things about Bayesian stats is that you can do things directly rather than indirectly, as in frequentist stats. For example, in frequentist stats you can't attach a probability to a hypothesis, so you can't talk about the probability of the hypothesis given the data. Instead, you have to mess around with the probability of the data given the hypothesis, which is not really what you want. Bayesian hypothesis testing is thus very simple in principle (though the sums may get hard in practice). You attach a prior probability to the hypothesis, multiply by the likelihood and divide by the probability of he evidence to normalise it. The point I was making was that probabilities of zero and one make poor choices as priors. (I am not saying that Bayesian stats generally has a problem with zero and one as probabilities, just when they are used as priors.) Your mention of linear models and so on suggests that you are thinking in terms of Bayesian methods of parameter estimation, whereas I was thinking in terms of Bayesian hypothesis testing. 15:28, 20