Noah Smith is having fun with automatic priors, pointing out that the reasonable person's prior on personal immortality is that you got it because you ain't dead yet.
Consider Proposition H: "God is watching out for me, and has a special purpose for me and me alone. Therefore, God will not let me die. No matter how dangerous a threat seems, it cannot possibly kill me, because God is looking out for me - and only me - at all times."Frequentists may disagree, bodycounts tell a bunny something, Noah points out that while there are other reasonable priors, how to determine which one should be used appears to be a religious matter. OTOH, there are people, particularly teenage boys who use Proposition H daily.
Suppose that you believe that there is a nonzero probability that H is true. And suppose you are a Bayesian - you update your beliefs according to Bayes' Rule. As you survive longer and longer - as more and more threats fail to kill you - your belief about the probability that H is true must increase and increase. It's just mechanical application of Bayes' Rule:
Eli and Socrates debated similar issues a while ago and Andrew Gelman about eight years ago pondered same
The fundamental objections to Bayesian methods are twofold: on one hand, Bayesian methods are presented as an automatic inference engine, and this raises suspicion in anyone with applied experience, who realizes that di erent methods work well in different settings (see, for example, Little, 2006). Bayesians promote the idea that a multiplicity of parameters can be handled via hierarchical, typically exchangeable, models, but it seems implausible that this could really work automatically. In contrast, much of the work in modern non-Bayesian statistics is focused on developing methods that give reasonable answers using minimal assumptions.Lars Syll riffs off Smith with a little less patience noting that as a religion Bayesianism is dangerous. The right to carry automatic priors can produce nonsense. James Annan showed this with Myles Allen's way to wide uniform prior, and the recent discussion about Nic Lewis' attempt to mangle C14 dating priors should caution the Bayesians.
The second objection to Bayes comes from the opposite direction and addresses the subjective strand of Bayesian inference: the idea that prior and posterior distributions represent subjective states of knowledge. Here the concern from outsiders is, first, that as scientists we should be concerned with objective knowledge rather than subjective belief, and second, that it's not clear how to assess subjective knowledge in any case.
Beyond these objections is a general impression of the shoddiness of some Bayesian analyses, combined with a feeling that Bayesian methods are being oversold as an allpurpose statistical solution to genuinely hard problems. Compared to classical inference, which focuses on how to extract the information available in data, Bayesian methods seem to quickly move to elaborate computation. It does not seem like a good thing for a generation of statistics to be ignorant of experimental design and analysis of variance, instead becoming experts on the convergence of the Gibbs sampler.
Long live frequentism, at least when there is enough data.