Abstracl.A mathematical analysis is made for the operation of a threshohl-type statistical pattern recognition system, and explicit expressions of the error rates for statistical independence among the nmsks are derived.Analogous expressions are presented for a more complex mode of operation using probability density curves instead of thresholds.The quantitative advantages of the latter system are exhibited.The effect of internal correlations in both methods is discussed.A third analysis is presented for an improved form of threshold device using optimal threshold positions for every mask; its error rate is compared with the density-curve system.A special case of this general formula is shown to agree, when differently interpreted, witt, a result obtained by Golay for detection of weak communication signals.The formulas also furnish a convenient method for measuring overa|l or effective correlation in a system.A method is suggested to reduce the storage requirements of the more complex method to that of the threshold devices, and a recommendation made to exploit the superior capabilities of the density-curve method.