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orthonormal comments on Bayes' rule =/= Bayesian inference - Less Wrong
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There are two slightly different meanings of what it is to be a "Bayesian": philosophically, there is a Bayesian interpretation of probability theory, and practically, there are Bayesian methods in statistics. I see Felsenstein as saying that, even if one is a Bayesian philosophically, one ought to practise as a likelihoodist.
In original research, I agree; there is not much point in reporting posteriors. Certainly there's no point in reporting them without also reporting the original priors, but better just to report the likelihoods and let readers supply their own priors.
On the other hand, in summaries for a broad readership, the posteriors are the most important result to report. Now most readers don't have the expertise to bring their own priors, so you have to give them yours. And then do the calculation for them.
Good point. It would be irresponsible to publish a news item that "the Prime Minister's support for this bill is three times more likely if he is, in fact, a lizard alien than if he is a human" without noting that the prior probability for him being a lizard alien is pretty low.
And yet they do this all the frigging time in medical stories, as documented extensively on, for instance, Bad Science.