In the phrase "the correct one", I have a problem with the word "the". See the discussion of the Bertrand paradox in krey's links.

For a specific example: I want to set a prior (an improper prior is okay!) for a constant in an Arrhenius equation for a chemical reaction. Oversimplified the equation looks like "r = A * exp(T/T0)". Oversimplify more, and pretend that T0 is known but I know nothing about A. Do I set a flat prior on A? But what if I instead chose to write the equation as "r = exp(T/T0 + a)". It's the same equation; A = exp(a). But the flat prior on a is not equivalent to the flat prior on A. Which do I choose?