  In this paper, two new classes of lower bounds on the probability of error
for $m$-ary hypothesis testing are proposed. Computation of the minimum
probability of error which is attained by the maximum a-posteriori probability
(MAP) criterion is usually not tractable. The new classes are derived using
Holder's inequality and reverse Holder's inequality. The bounds in these
classes provide good prediction of the minimum probability of error in multiple
hypothesis testing. The new classes generalize and extend existing bounds and
their relation to some existing upper bounds is presented. It is shown that the
tightest bounds in these classes asymptotically coincide with the optimum
probability of error provided by the MAP criterion for binary or multiple
hypothesis testing problem. These bounds are compared with other existing lower
bounds in several typical detection and classification problems in terms of
tightness and computational complexity.
