[mattkrause]

There are situations where one does care about long-run frequencies though, right?

Perhaps something like quality control, where we want a procedure that only rejects 5% of within-spec parts?

[gbrown]

Sure, but there's nothing which would prevent you from addressing that from a Bayesian perspective. In fact, Bayesian particle filtering techniques would probably be a great tool for "on-line" quality assurance.