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 /spl epsiv/ denote the minimum probability of error incurred in estimating X from Y. It is shown that /spl epsiv//spl ges//sub 0/spl les//spl alpha//spl les/1//sup sup/(1-/spl alpha/)P(/spl pi/(X|Y)/spl les//spl alpha/) where /spl 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 (1994).