The biggest Bayesian objection to so-called “classical” statistics—p-values and confidence intervals, not the online-learning stuff with non-probabilistic guarantees—is that they provide the correct answer to the wrong question. For example, confidence intervals are defined as random intervals with certain properties under the sampling distribution. These properties are “pre-data” guarantees; the confidence interval procedure offers no guarantees to the one specific interval one calculates from the actual realized data one observes.
I’m personally pretty comfortable with such “pre-data” guarantees as long as they’re sufficiently high probability (e.g. if they hold with probability 99.9999%, I’m not too concerned that I might be unlucky for this specific interval). But I’m not necessarily that interested in defending p-values. I don’t dislike them, and I think they can be quite useful in some situations, but they’re not the best thing ever.
I do, however, think that concentration bounds are really good, which I would consider to be a sort of conceptual descendant of p-values (but I have no idea if that’s actually how they were developed historically).
The biggest Bayesian objection to so-called “classical” statistics—p-values and confidence intervals, not the online-learning stuff with non-probabilistic guarantees—is that they provide the correct answer to the wrong question. For example, confidence intervals are defined as random intervals with certain properties under the sampling distribution. These properties are “pre-data” guarantees; the confidence interval procedure offers no guarantees to the one specific interval one calculates from the actual realized data one observes.
I’m personally pretty comfortable with such “pre-data” guarantees as long as they’re sufficiently high probability (e.g. if they hold with probability 99.9999%, I’m not too concerned that I might be unlucky for this specific interval). But I’m not necessarily that interested in defending p-values. I don’t dislike them, and I think they can be quite useful in some situations, but they’re not the best thing ever.
I do, however, think that concentration bounds are really good, which I would consider to be a sort of conceptual descendant of p-values (but I have no idea if that’s actually how they were developed historically).