Generalized mutual information and their reference prior under Csizar f-divergence

In Bayesian theory, the role of information is central. The influence exerted by prior information on posterior outcomes often jeopardizes Bayesian studies, due to the potentially subjective nature of the prior choice. When the studied model is not enriched with sufficiently a priori information, the reference prior theory emerges as a proficient tool. Based on the mutual information criterion, the theory handles the construction of a non informative prior whose choice could be called objective. We unveil an original analogy between reference prior theory and Global Sensitivity Analysis, from which we propose a natural generalization of the mutual information definition. A class of our generalized metrics is studied and our results reinforce the Jeffreys' prior choice which satisfies our extended definition of reference prior.