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A Tight Upper Bound on the Bayesian Probability of Error
February 1994 (vol. 16 no. 2)
pp. 220-224

In this paper, we present a new upper bound on the minimum probability of error of Bayesian decision systems for statistical pattern recognition. This new bound is continuous everywhere and is shown to be tighter than several existing bounds such as the Bhattacharyya and the Bayesian bounds. Numerical results are also presented.

[1] T. Kailath, "The divegence and Bhattacharyya distance measures in signal detection,"IEEE Trans. Comm. Tech., vol. COM-15, pp. 52-60, Feb. 1967.
[2] H. Chernoff, "A measure of asymptotic efficiency for tests of a hypothesis based on a sum of observations,"Ann. Math. Stat., vol. 23, pp. 493-507, 1952.
[3] C. H. Chen, "Theoretical comparison of a class of feature selection criteria in pattern recognition,"IEEE Trans. Comput., vol. C-20, pp. 1054-1056, Sept. 1971.
[4] C. H. Chen, "On information and distance measures, error bounds, and feature selection,"Inform. Sci., vol. 10, pp. 159-171, 1976.
[5] M. E. Hellman, "Probability of error, equivocation, and Chernoff bound,"IEEE Trans. Inform. Theory, vol. 16, pp. 368-372, July 1970.
[6] P. A. Devijver, "On a new class of bounds on Bayes risk in multihypothesis pattern recognition,"IEEE Trans. Comput., vol. C-23, pp. 70-80, Jan. 1974.
[7] D. E. Boekee and J. C. A. Van der Lubbe, "Some aspects of error bounds in feature selection,"Pattern Recognition, vol. 11, pp. 353-360, 1979.
[8] T. Ito, "Approximate error bounds in pattern recognition,"Machine Intell., vol. 7, pp. 369-376, 1972.
[9] G. T. Toussaint, "On the divergence between two distributions and the probability of misclassification of several decision rules," inProc. Second Int. Joint Conf. Pattern Recognition, Copenhagen, Denmark, Aug. 1974.
[10] M. Ben-Bassat, "Use of distance measures, information measures, and error bounds in feature evaluation," inHandbook of Statistics, vol. 2, P. R. Krishnaiah and L. N. Kanal, Eds. Amsterdam, The Netherlands: North-Holland, 1982, ch. 35, pp. 773-791.
[11] L. Devroye, "On the asymptotic probability of error in nonparametric discrimination,"Ann. Stat., vol. 9, no. 6, pp. 1320-1327, 1981.
[12] S. M. Ali and S. D. Silvey, "A general class of coefficients of divergence of one distribution from another,"J. Roy. Statist. Soc., series B, vol. 28, pp. 131-143, 1966.
[13] H. L. Van Trees,Detection, Estimation, and Modulation Theory, Vol. I. New York: Wiley, 1968.
[14] A. K. Jain, "On an estimate of the Bhattacharyya distance,"IEEE Trans. Syst., Man, Cybern., Nov. 1976.
[15] A. Djouadi, O. Snorrason, and F. D. Garber, "The quality of training sample estimates of the Bhattacharyya coefficient,"IEEE Trans. Pattern Anal. Machine Intell., vol. 12, pp. 92-97, Jan. 1990.
[16] J. L. Devore,Probability and Statistics for Engineering and the Sciences. New York: McGraw-Hill, 1990.
[17] H. V. Poor and J. B. Thomas, "Applications of Ali-Silvey distance measures in the design of generalized quantizers for binary decision systems,"IEEE Trans. Commun., vol. COM-25, pp. 893-900, Sept. 1977.
[18] H. V. Poor, "Fine quantization in signal detection and estimation,"IEEE Trans. Inform. Theory, vol. 34, no. 5, Sept. 1988.
[19] W. A. Hashlamoun, "Applications of distance measures and probability of error bounds to distributed detection systems," Ph.D. dissertation, Syracuse Univ., May 1991.

Index Terms:
pattern recognition; Bayes methods; probability; decision theory; statistical pattern recognition; tight upper bound; Bayesian probability; minimum error probability
W.A. Hashlamoun, P.K. Varshney, V.N.S. Samarasooriya, "A Tight Upper Bound on the Bayesian Probability of Error," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 2, pp. 220-224, Feb. 1994, doi:10.1109/34.273728
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