Updating information based on generalized credal sets. Part 2: General case

Abstract

In the first part of this paper, we have considered: a) generalized credal sets on the powerset of a finite set X; b) their general definition allowing a generalized credal set to be not convex; c) the justification of basic aggregation rules on generalized credal sets; d) ways of updating information. The second part is devoted to the solutions of the above problems for the general case, when generalized credal sets are defined on arbitrary measurable spaces. In addition, we prove that the conditionals after updating of a generalized credal set could be chosen ratio-equivalent. This result confirms the thesis by R.A. Fisher, which says that the likelihood function is defined uniquely up to a positive coefficient.