= Jeffreys prior
{c}
{title2=$\pi_J(\theta)\propto\sqrt{\det I(\theta)}$}
The Jeffreys prior uses the square root of the determinant of the <Fisher information matrix> as a parameter-density kernel. It is invariant under smooth one-to-one reparameterization, since the information and density Jacobians transform compatibly. It may be an <improper prior>; invariance does not guarantee <posterior propriety>. With nuisance parameters, a scalar conditional Jeffreys prior and the joint Jeffreys prior need not coincide.
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