View source for 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|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.

[[Category:Mathematics]]
[[Category:Probability]]