Oh dear indeed

From one of Tim Worstall’s “Oh dear” posts:

Maybe inequality and poverty in modern Britain are important and maybe they’re not. It’s entirely possible to argue it either way and to a large extent depends upon your Bayesian priors.

So naturally I had to reply,

Actually this is a value judgment and would be expressed through a utility function. Bayesian priors (and posteriors) are probability distributions expressing subjective degrees of certainty over parameters of interest.

No indication thus far that the blog author has taken this on board…

Is it better that Bayesian concepts are invoked incorrectly rather than not at all? I believe so, but we must continue to strive towards fuller understanding of them amongst non-statisticians. Because otherwise we have to deal with things like this:

First, what did you think was the probability of success in Afghanistan before the mission began? This is the prior probability, which we’ll call Ps. The probability of failure, Pf, is one minus this.

Second, what is the probability that we’d see the number of deaths we have, if the mission were succeeding? Call this Pd|s. One minus this gives us Pd|f. [emphasis mine, calculation thankfully not]

Again, comments to the contrary had no effect on deflecting the author in his enthusiasm on this occasion. Oh dear.

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2 Comments »

  1. Ah, you’re missing something.

    “Bayesian priors” has been used for some time (it originated with Chris Dillow) as a slang for “prejudices”.

    Nothing to do with mathematics or statistics at all, just a little bit of blogging argot.

    • Mr. Bayes said

      You, Sir, are quick off the mark.

      Is Chris Dillow the fellow responsible for the last quote in my post? Then I am not placated at all. His mistake was magnitudes worse than yours!

      I am perfectly happy with slang, but I have to point out when it’s misleading. Your beliefs in the “importance” of inequality in society is very likely to be a value judgement, not a state parameter, and so it will not be updated in the light of new data (i.e. it cannot become a “Bayesian posterior”!). Of course the boundary between the two is blurred because you might not be sure how much you care about, say, inequality in society, because you are not sure of its effects on other parameters which you care about; but this is still an uncertainty in the utility function.

      Utilities fit nicely into the Bayesian paradigm, but are certainly not exclusive to it. Mixing up their subjectivity with the subjective belief of system variables (only the latter of which are governed purely by my famous posthumous Theorem) is not recommended for the faint-hearted.

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