Statistical Hypothesis Testing and Lower Bounds to the Error Probability

Gonzalo Vazquez-Vilar, Adrià Tauste Campo, Albert Guillén i Fàbregas, Alfonso Martinez

Published 2014-11-12Version 1

We prove two alternative expressions for the error probability of Bayesian M-ary hypothesis testing. The first expression is related to the error probability of binary hypothesis testing, and the second one to a generalization of the Verd\'u-Han lower bound. This result is used to characterize the error probability of the main problems in information theory and identify the steps where previous converse results are loose with respect to the actual probability of error.