lambdaphagy:

perversesheaf:

As someone interested in both philosophy and mathematics, I am disturbed by the rise of what I call “radical Bayesian,” or the belief that the standard probability axioms and Bayes’ rule together give us a complete description of how we ought to reason about the world (at least in principle). I…

Thanks for this post.  Three points to make about this, two minor and one major.  I haven’t read all of the replies to this yes, so forgive me if I’m repeating what others have already said.

About frequentist hypothesis testing, Fisherian p values are not the only option.  Neyman-Pearson testing would give you more power and conceptual coherence, since you have a concrete alternate hypothesis whose likelihood function you can also write down.

And technically, the p-value is the probability of a test statistic being at least as extreme as for your data, given the null.

But the real issue is: why can’t Bayesians use a stopping rule if that’s the correct model?

If I want to know about the bias of a coin flipped a given number of times, then my likelihood function is the usual binomial likelihood.

But if I include a stopping rule, then my likelihood function has changed because my event space has changed.  Certain outcomes are no longer possible, so I’ll have to assign them a probability of zero and renormalize.  Others would call me a pretty radical Bayesian, at least in my day job, and that’s what I would instinctively do.

W/r/t the last point: the difference is that in the case of the coin, the stopping rule (presumably) is about the coin – say, “stop when you get the first tails” (so that “HT” is possible but not “TH”).  But in the OP’s example, the stopping rule refers to the statistician’s own belief.  To incorporating that kind of stopping rule the Bayesian reasoner would need to include its own beliefs as part of the sample space.

(As mentioned earlier I am not sober so I may being thinking badly)

(via lambdaphagy)