Bayesian philosophers (among others) have analogous versions of the criticism in my April 28 blogpost: error probabilities (associated with inferences to hypotheses) may conflict with chosen posterior probabilities in hypotheses. Since it’s Saturday night let’s listen in to one of the comedy hours at the Bayesian retreat (note the sedate philosopher’s comedy club backdrop):
Did you hear the one about the frequentist error statistical tester who inferred a hypothesis H passed a stringent test (with data x)?
The problem was, the epistemic probability in H was so low that H couldn’t be believed! Instead we believe its denial H’! So, she will infer hypotheses that are simply unbelievable!
So clearly the error statistical testing account fails to serve in an account of knowledge or inference (i.e., an epistemic account). However severely I might wish to say that a hypothesis H has passed a test, the Bayesian critic assigns a sufficiently low prior probability to H so as to yield a low posterior probability in H[i]. But this is no argument about why this counts in favor of, rather than against, their Bayesian computation as an appropriate assessment of the warrant to be accorded to hypothesis H.
To begin with, in order to use techniques for assigning frequentist probabilities to events, their examples invariably involve “hypotheses” that consist of asserting that a sample possesses a characteristic, such as “having a disease” or “being college ready” or, for that matter, “being true.” This would not necessarily be problematic if it were not for the fact that their criticism requires shifting the probability to the particular sample selected—for example, a student Isaac is college-ready, or this null hypothesis (selected from a pool of nulls) is true. This was, recall, the fallacious probability assignment that we saw in Berger’s attempt, later (perhaps) disavowed. Also there are just two outcomes, say s and ~s, and no degrees of discrepancy from H. Read more
