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 epsilon denote the minimum probability of error incurred in estimating X from Y. It is shown that [GRAPHICS] where pi(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.