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.

General theory of processes (msc 60G07), Applications of stochastic analysis (to PDE, etc.) (msc 60H30), Theory of statistical experiments (msc 62B15), Measures of information, entropy (msc 94A17)
Logistics (theme 3), Energy (theme 4)
CWI. Probability, Networks and Algorithms [PNA]

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.