Jeffreys Prior - Attributes

Attributes

From a practical and mathematical standpoint, a valid reason to use this non-informative prior instead of others, like the ones obtained through a limit in conjugate families of distributions, is that it is not dependent upon the set of parameter variables that is chosen to describe parameter space.

Sometimes the Jeffreys prior cannot be normalized, and thus one must use an improper prior. For example, the Jeffreys prior for the distribution mean is uniform over the entire real line in the case of a Gaussian distribution of known variance.

Use of the Jeffreys prior violates the strong version of the likelihood principle, which is accepted by many, but by no means all, statisticians. When using the Jeffreys prior, inferences about depend not just on the probability of the observed data as a function of, but also on the universe of all possible experimental outcomes, as determined by the experimental design, because the Fisher information is computed from an expectation over the chosen universe. Accordingly, the Jeffreys prior, and hence the inferences made using it, may be different for two experiments involving the same parameter even when the likelihood functions for the two experiments are the same—a violation of the strong likelihood principle.