I asked my professor, "But don't we want to know the probability of the hypothesis we're testing given the data, not the other way around?" The reply was something about how this was the best we could do.

One senses that the author (the one in the student role) neither has understood the relative-frequency theory of probability nor has performed any empirical research using statistics--lending the essay the tone of an arrogant neophyte. The same perhaps for the professor. (Which institution is on report here?) Frequentists reject the very concept of "the probability of the theory given the data." They take probabilities to be objective, so they think it a category error to remark about the probability of a theory: the theory is either true or false, and probability has nothing to do with it.

You can reject relative-frequentism (I do), but you can't successfully understand it in Bayesian terms. As a first approximation, it may be better understood in falsificationist terms. (Falsificationism keeps getting trotted out by Bayesians, but that construct has no place in a Bayesian account. These confusions are embarrassingly amateurish.) The Fischer paradigm is that you want to show that a variable made a real difference--that what you discovered wasn't due to chance. However, there's always the possibility that chance intervened, so the experimenter settles for a low probability that chance alone was responsible for the result. If the probability (the p value) is low enough, you treat it as sufficiently unlikely not to be worth worrying about, and you can reject the hypothesis that the variable made no difference.

If, like I, you think it makes sense to speak of subjective probabilities (whether exclusively or along with objective probabilities), you will usually find an estimate of the probabilities of the hypothesis given the data, as generated by Bayesian analysis, more useful. That doesn't mean it's easy or even possible to do a Bayesian analysis that will be acceptable to other scientists. To get subjective probabilities out, you must put subjective probabilities in. Often the worry is said to be the infamous problem of estimating priors, but in practice the likelihood ratios are more troublesome.

Let's say I'm doing a study of the effect of arrogance on a neophyte's confidence that he knows how to fix science. I develop and norm a test of Arrogance/Narcissism and also an inventory of how strongly held a subject's views are in the philosophy of science and the theory of evidence. I divide the subjects in two groups according to whether they fall above or below the A/N median. I then use Fischerian methods to determine whether there's an above-chance level of unwarranted smugness among the high A/N group. Easy enough, but limited. It doesn't tell me what I most want to know, how much credence should I put in the results. I've shown there's evidence for an effect, but there's always evidence for some effect: the null hypothesis, strictly speaking, is always false. No two entities outside of fundamental physics are exactly the same.

Bayesian analysis promises more, but whereas other scientists will respect my crude frequentist analysis as such—although many will denigrate its real significance—many will reject my Bayesian analysis out of hand due to what must go into it. Let's consider just one of the factors that must enter the Bayesian analysis. I must estimate the probability that that the 'high-Arrogance' subjects will score higher on Smugness if my theory is wrong, that is, if arrogance really has no effect on Smugness. Certainly my Arrogance/Narcissism test doesn't measure the intended construct without impurities. I must estimate the probability that all the impurities combined or any of them confound the results. Maybe high-Arrogant scorers are dumber in addition to being more arrogant, and that is what's responsible for some of the correlation. Somehow, I must come up with a responsible way to estimate the probability of getting my results if Arrogance had nothing to do with Smugness. Perhaps I can make an informed approximation, but it will be unlikely to dovetail with the estimates of other scientists. Soon we'll be arguing about my assumptions--and what we'll be doing will be more like philosophy than empirical science.

The lead essay provides a biased picture of the advantages of Bayesian methods by completely ignoring its problems. A poor diet for budding rationalists.