Prior Information in a Jeffreys Prior:
Distinction between invariance and non-informativeness
Yasuharu Okamoto
Summary
Most Bayesians favor a Jeffreys prior as a non-informative one. This interpretation of non-informativeness of a Jeffreys prior is based on invariance. It is pointed out here, however, that a Jeffreys prior is not non-informative. The condition of invariance of probability under parameter transformation was examined, and Jeffreys priors were characterized to be related to each other in a way that they satisfy the condition of invariance. But invariance and non-informativeness must be distinguished. The fact that a Jeffreys prior in item response theory depends on information about an examinee was pointed out. This fact indicates that a Jeffreys prior is not non-informative, although the probability that it defines is invariant.