A lower bound on the probability of error in multihypothesis testing

Consider two random variables X and Y, where X is finitely (or countably-infinitely) valued, and where Y is arbitrary. Let ε denote the minimum probability of error incurred in estimating X from Y. It is shown that ε⩾_0⩽α⩽1^sup (1-α)P(π(X|Y)⩽α) where π(X|Y) denotes the posterior probability of X given Y. This bound finds information-theoretic applications in the proof of converse channel coding theorems. It generalizes and strengthens previous lower bounds due to Shannon, and to Verdu and Han (1994)