Meta-Bound on Lower Bounds of Bayes Risk in Parameter Estimation

Abstract

Information-theoretic lower bounds of the Bayes risk have been investigated for a problem of parameter estimation in a Bayesian setting. 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 mutual information, Sibson's α-mutual information, f-divergence, 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 inequality.