Statistical Causality And Measurable Separability Of Sigma-Algebras

In this paper we consider a concept of statistical causality, based on Granger's definition of causality and analyze the relationships between given causality and the concept of measurable separability of sigma-algebras. The measurable separability of sigma-algebras is defined in Florens et al. (1990). We give a generalization of that definition for flows of information represented by filtrations and consider some properties of measurable separability that are directly connected to the concept of statistical causality. Also, we apply some of these results on Bayesian experiment. (C) 2021 Elsevier B.V. All rights reserved.