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An Invariant Form for the Prior Probability in Estimation Problems

Harold Jeffreys
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 186, No. 1007 (Sep. 24, 1946), pp. 453-461
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/97883
Page Count: 9
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An Invariant Form for the Prior Probability in Estimation Problems
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Abstract

It is shown that a certain differential form depending on the values of the parameters in a law of chance is invariant for all transformations of the parameters when the law is differentiable with regard to all parameters. For laws containing a location and a scale parameter a form with a somewhat restricted type of invariance is found even when the law is not everywhere differentiable with regard to the parameters. This form has the properties required to give a general rule for stating the prior probability in a large class of estimation problems.

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