Jeffreys Prior

The Jeffreys prior is a rule for constructing prior probability distributions that claims to encode maximum ignorance — an objective Bayesian method developed by the geophysicist and statistician Harold Jeffreys in the 1940s. The rule sets the prior proportional to the square root of the determinant of the Fisher information matrix, which means the prior gives more weight to parameter regions where the data would be more informative. Jeffreys intended this as a way to let the data speak without the statistician's subjective biases dominating the inference, but the prior is not as objective as it appears: the construction depends on the parameterization of the model, and a reparameterization can change the prior entirely. This parameterization dependence reveals that even supposedly objective priors smuggle in assumptions — in this case, assumptions about what counts as a natural way to describe the problem.