Expressing Prior Ignorance of a Probability Parameter

If p is an unknown probability parameter, prior ignorance of its value is appropriately expressed by the prior probability density distribution ) 1 ( 1 ) ( p p p f − ∝ . That is the only distribution that remains invariant under transformations that convert the original inference problem into another that should look identical to a truly ignorant observer. This invariance principle for specifying an ignorant prior distribution, pioneered in the writings of the late E.T. Jaynes, is contrasted with the principle of “data translation” as set forth by Box and Tiao—a principle that typifies alternative approaches to “noninformative” prior distributions.