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    $\begingroup$ +1: Good answer. But, why doesn't the Jeffreys' prior represent ignorance about the value of the parameters? $\endgroup$ Commented Oct 9, 2012 at 5:50
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    $\begingroup$ Because it is not even a distribution. It is paradoxical to claim that a distribution reflects ignorance. A distribution always reflects information. $\endgroup$ Commented Oct 9, 2012 at 6:21
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    $\begingroup$ Another reference: projecteuclid.org/… $\endgroup$ Commented Oct 9, 2012 at 6:22
  • $\begingroup$ @StéphaneLaurent: One must have some belief even in a state of total ignorance. Whatever your posterior is minus whatever likelihood is induced by your data is the belief that you are assuming in that state of ignorance. The intuitive principle that must be respected when deciding that belief is that it should be invariant under changes of labels (including reparametrization). I'm not sure, but I think that principle alone (in all its possible interpretations — maximum entropy, invariant reparametrization, etc.) always decides the belief. $\endgroup$ Commented Jan 30, 2015 at 7:24
  • $\begingroup$ Therefore, when one says "a distribution reflects ignorance", one means that the distribution concords with this principle. $\endgroup$ Commented Jan 30, 2015 at 7:25