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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.

 

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