Bayesian probability

I recently blogged about The cosmic landscape, where I made some remarks about the relationship between Bayes theorem, the anthropic principle, and the cosmic landscape. I pointed out that the anthropic principle is a consequence of Bayes theorem applied to systems of interacting parts (e.g. observers and the observed). Thus our existence as observers is always part of the overall set of experimental observations that should be taken into account when constructing candidates for the "laws of physics". I would have thought that this much was obvious!

Not so, apparently. Such is the strength of conviction by some people that the anthropic principle is pseudo-scientific (e.g. many postings here!) that they choose to criticise the Bayesian approach, presumably because it is a rigorous approach to drawing inferences, which is thus justifiably perceived as a credible threat to their anti-anthropic stance. To assert that the Bayesian approach or the anthropic principle is pseudo-scientific (or a "dangerous idea", or whatever) won't make them go away, because they are more rigorous than some people appear to realise.

A particularly "fine" example of such misplaced criticism is by Luboš Motl here, because it appears to be based on an undergraduate level of understanding of the Bayesian approach, including all of the philosophical mumbo-jumbo that gets taught about the frequentist versus the Bayesian versions of probability. I too went through a frequentist versus Bayesian stage of my learning, mostly due to the influence of the otherwise excellent MaxEnt series of workshops . A good paper to read that uses an "axiomatic" approach to understanding all of this is: Cox R T, "Probability, frequency and reasonable expectation", Am. J. Phys., 1946, 14(1), 1-13.

It is such a pity when an intelligent scientist (e.g. Luboš Motl) chooses to criticise something by making apparently sage pronouncements too far outside their own area of expertise. Yes, you might read a text book one evening and then pass an exam the next day, but this limits you to what is in the text book, doesn't it? Experienced researchers know that the real expertise is not recorded as simple bite-sized entries in text books, but is accumulated over years of careful reflection about a subject.

Or maybe I have fallen for a troll, where Luboš Motl tricks me into mentioning his name (more than once!) in my blog, thus helping him on towards world domination.