- Hellinger and information processes in filtered experiments, part I: general concepts
- Document type
- Working paper
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
In this paper we define randomized filtered experiments with an abstract parameter space and analyze some properties of this concept. To that end we introduce three special probability measures that dominate a given expirement, called geodesic measure, arithmetic and geometric mean measures, and a generalized Hellinger process for an abstract family of probability measures. We also introduce and analyze the Kullback-Leibler information process of a posterior distribution on the parameter space with respect to a prior and give an expression for this in terms of the concepts given above.