Jeffreys prior is a type of non-informative prior probability distribution used in Bayesian statistics. It is designed to be invariant under reparameterization, which means that the prior distribution should not change if the parameters are transformed. The Jeffreys prior is derived from the likelihood function of the data and is based on the concept of the Fisher information.
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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.