More often than not science (and statistics especially) is counter-intuitive. Since the human world is built on and maintained by science (and to a larger and larger extent, on and by statistics), this should tell us something about the value of “common sense” (of which I am not particularly fond of). I was just reminded of that by an excellent paper by Zhu and Lu (2004), where the authors present, with students in mind, the strongly counter-intuitive/confusing/hard-to-believe, case of the uninformative prior distribution in the context of Bayesian estimation related to the apparently simple case of a Bernoulli random variable where we want to estimate the probability that the variable will take the value 1.

Now almost everybody (myself included), using -what else- common sense, view a Uniform prior (ranging in (0,1) in our case), as the bona fide uninformative one (which goes back to The Principle of Insufficient Reason). In our case, using such a prior distribution reflects a prior belief that the probability we want to estimate can take any value in (0,1) with equal probability –**how more uninformative can you be**?

Oh, but you can. In fact Zhu and Lu paper shows clearly that for the case at hand, such a prior influences rather distinctly the posterior results -and so it is not-uninformative at all. They also derive the actual uninformative prior for this case.

Download the paper :

Zhu and Lu – Non Informative priors for Bernoulli rv

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that’s really interesting. Thank you.