In a filtered statistical experiment a priori and a posteriori probability measures are defined on an abstract parametric space. The information in the posterior, given the prior, is defined by the usual Kullback-Leibler formula. Certain properties of this quantity is investigated in the context of so-called arithmetic and geometric measures and arithmetic and geometric processes. Interesting multiplicative decompositions are presented that involve Hellinger processes indexed both by prior and by posterior distributions.

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CWI
CWI. Probability, Networks and Algorithms [PNA]
Stochastics

Dzhaparidze, K.O, Spreij, P.J.C, & Valkeila, E. (1998). On a posterior information process for parametric families of experiments. CWI. Probability, Networks and Algorithms [PNA]. CWI.