On Meta-Bound for Lower Bounds of Bayes Risk

For the problem of parameter estimation in a Bayesian setting, information-theoretic lower bounds of the Bayes risk have been investigated. Previous studies have proven the lower bound of the Bayes risk in a different manner and characterized the lower bound via different quantities such as the mutual information, Sibson’s α-mutual information, and Csiszár’s f-informativity. In this paper, we introduce an inequality called a "meta-bound for lower bounds of the Bayes risk" and show that the previous results can be derived from this bound.