prior probability finally got around to reading their critique and is now ready to file this reply:
First, Marcus & Davis try to take Silver down a notch by noting that Bayesian methods are not new, that the Bayesian approach to probability “is built around a two-hundred-fifty-year-old theorem that is usually taught in the first weeks of college probability courses.” True, Baryes’ famous theorem has been around a long time, but that is not the whole truth. The whole truth is that the intellectual history of mathematics and statistics has been openly hostile and dismissive of Bayesian methods until recently.
Next, after grudgingly conceding the superiority of Bayesian reasoning in many situations, Marcus & Davis state (incorrectly) that “the Bayesian approach is much less helpful when there is no consensus about what the prior probabilities should be.” But this is plain wrong, and shows that Marcus & Davis missed one of the main take-away lessons of Silver’s book: it doesn’t really matter what your priors are so long as you update them whenever you receive new evidence regarding the matter you are uncertain about.
Last, Marcus & Davis attempt to mount a rearguard defense of R.A. Fisher’s frequency approach to probability, long the dominant approach in modern statistics, noting that “the advantage of Fisher’s approach … is that it sidesteps the problem of estimating priors where no sufficient information exists.” (By the way, what is it with the frequentists and their unwholesome obsession with priors?) But Marcus & Davis are being disingenuous here, for they themselves “sidestep” the major flaws with Fisher’s frequentist approach, especially its ad hoc nature and the fact that most events about which we are uncertain do not lend themselves to a frequency analysis.
Because Nate Silver’s book is such an important work, prior probability will soon be conducting a chapter-by-chapter review of The Signal and the Noise in future posts.