An invariant form for the prior probability in estimation problems. (English) Zbl 0063.03050

Jeffreys, Harold

Proc. R. Soc. Lond., Ser. A 186, 453-461 (1946).

Summary: 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.

MSC:

62-XX

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