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

General Classes of Lower Bounds on the Probability of Error in Multiple Hypothesis Testing