Bayes' error probability for noisy and imprecise measurement in pattern recognition

The problem of statistical pattern recognition with noisy or imprecise feature measurements is considered. Exact analytical expression for the probability of misclassification under this condition has been found for multiclass multivariate systems. It is proved that the probability of error exceeds that of the ideal case. For the special case of two classes, the a priori conditional probability density functions are assumed to be normal along with two cases of feature measurement error, namely, normal and uniform probability density functions. Monotonicity of the misclassification probability with measurement error variance is shown. Numerical results have been presented for both cases over workable range of parameters. The study is useful in practical pattern recognition problems.