But wasn't the very idea of "subjective" probability to take our psychological intuitions as the primary source of probability valuations? There seem to be conflicting agendas here. But on the other hand, if we give up the simplistic rationalism of Bayes, won't we then diverge from scientific (not to mention mathematical) probability, carving out a special theory that's only relevant to psychology? — Sophisticat
I read a few things on likelihoodism and other ideas of what is the 'right way' to show that data favours a hypothesis against a (set of) competing hypothesis. — fdrake
In my view, if there is a conflict of the intuition with something that is already unambiguously formalised, go with the formalisation. — fdrake
I am sorry, my statistics and hypothesis testing background is too basic and rusty to fully appreciate your comments. I didn't mean to advocate likelyhoodism though - I only mentioned it as an example of Bayesians not being satisfied with prior probabilities and seeking ways to avoid them while still preserving what they think are Bayesianism's advantages. — Sophisticat
Without arguing which is better, this should hopefully clear up (to some degree) my disagreement with Jeremiah and perhaps provide something interesting to think about for the mathematically inclined. — fdrake
The thrust of the comments is that contemporary statistics uses plenty of methods and mathematical objects that are not consistent with contemporary philosophy of statistics' accounts of evidential content and the methods and objects used to analyse it. One response would be 'so much the worse for statistics', but I think it's so much the worse for philosophy of statistics since these methods observably work. — fdrake
I think whether Bayesian models of the mind or of learning in general are accurate in principle is mostly orthogonal to interpretations of probability. Would be worth another thread though. — fdrake
Well, isn't the entire thrust of the Bayesian (aka epistemic) interpretation to psychologize probability?
I think the discrepancy in interpretations lends itself due to the possibility of hidden variables. Is this something that is considered in probability theory because it goes to the heart of the issue in my opinion?
Can you elaborate a little please? Are you suggesting that hypothesis tests are always invalid under a strict Bayesian approach, or only that the vast majority of them are?If you're a strict Bayesian the vast majority of applied research is bogus (since it uses hypothesis tests). — fdrake
If I have a null hypothesis that a population parameter mu has value q and calculate that, conditional on the null hypothesis being true, the probability of statistic S from a randomly chosen sample of n elements having a value in set A is p, are you saying that making that statement is inconsistent with a Bayesian view?
I think so. But I don't think this accounts for whether Bayesian approaches to AI and the mind are correct or not. In my view AI questions about Bayesian methods are 'does this statistical model learn in the same way humans do?' or 'is this statistical model something like what a conscious mind would do?', but epistemic questions are 'does this interpretation of probability make sense of how probability is used?' and 'does (list of properties of Bayesian inference) give a good normative account of how we ought to reason?'. — fdrake
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