A Bayesian Paradox ?

William M. Briggs post The Jeffreys-Lindley Paradox Isn’t

refers to this article at Science2.0 by Tommaso Dorigo

Ina  sense both seem to be saying the same thing but perhaps for different reasons. Dorigo concludes that there is no paradox because the two approaches are answering different questions – which is certainly the case from the numerical point of view but perhaps not the “moral” one. (ie the common “moral” question is “should we trust the detector?” and the two approaches do appear to give different answers.

My first stab at a response to Dorigo would be to suggest that a “proper” Bayesian approach (if there is one) should be constantly re-adjusting the priors in the light of observations to date. So by the time observation 1000000 rolls in here have already been many reasons (albeit not all independent of course) to abandon the 50% “delta function”. I haven’t given any rel thought to whether this would make a difference but my gut says it should.

As to Briggs, I need first to see how what he is saying differs essentially from Dorigo but, as usual, I find his talk of “the probability that T is true” to be off-putting at best. (Dorigo is less at fault for this because the specific context does give a sense of what that “probability” might mean whereas in Briggs discussion T is treated so abstractly as to give it no substance).

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