In this paper we present the foundations of Fully Probabilistic Design for the case when the Kullback-Leibler divergence is replaced by the Tsallis divergence. Because the standard chain rule is replaced by subadditivity, immediate backwards recursion is not available. However, by forming a fixed point iteration, we can establish a constructive proof of the existence of a solution to this problem, which also constitutes an algorithmic scheme that iteratively converges to this solution. This development can provide greater versatility in Bayesian Decision Making as far as adding flexibility to the problem formulation.
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