Tyler Cowen links to an article from 1999 by Mark Greenberg that discusses the so-called “doomsday argument,” which holds that there is there is a high probability that humanity will be extinct (or drastically reduce in population) soon, because if this were not true–if, for example, humanity were to continue with 10 billion people or so for the next few thousand years–then each of us would be among the first people to exist, and that’s highly unlikely.

Anyway, the (sociologically) interesting thing about this argument is that it’s been presented as Bayesian (see here, for example) but it’s actually not a Bayesian analysis at all! The “doomsday argument” is actually a classical frequentist confidence interval. Averaging over all members of the group under consideration, 95% of these confidence intervals will contain the true value. Thus, if we go back and apply the doomsday argument to thousands of past data sets, its 95% intervals should indeed have 95% coverage. If you look carefully at classical statistical theory, you’ll see that it makes claims about averages, not about particular cases.

However, this does not mean that there is a 95% chance that any particular interval will contain the true value. Especially not in this situation, where we have additional subject-matter knowledge. That’s where Bayesian statistics (or, short of that, some humility about applying frequentist inferences to particular cases) comes in. The doomsday argument is pretty silly (and also, it’s not Bayesian). Although maybe it’s a good thing that Bayesian inference has such high prestige now that it’s being misapplied in silly ways. That’s a true sign of acceptance of a scientific method.