Relative Informativity and a Priori Information in the Category of Linear Information Transformers

This paper continues the study of general properties of categories of information transformers for linear stochastic information transformers. It introduces and studies the concept of relative informativity, which emerges in decision-making problems with a priori information. The problem of comparison of relative informativity leads to the notion of normal relative equivalent, which represents, in a certain sense, the maximum information that can be obtained in an experiment and provides a simple algebraic criterion for comparing relative informativity of various experiments. Many fundamental concepts of probability and statistics such as random element, distribution, joint distribution, and conditional transition distribution are defined and studied in terms of categories of information transformers. All the introduced notions are applied to the study of decision-making problems with a priori information. The proposed approach is similar to the Bayes approach in statistics. Among other results, the Bayes principle for the category of linear stochastic information transformers is derived.