Linear discriminant analysis (LDA) is a powerful technique in pattern recognition to reduce the dimensionality of data vectors. It maximizes discriminability by retaining only those directions that minimize the ratio of within-class and between-class variance. In this paper, using the same principles as for conventional LDA, we propose to employ uncertainties of the noisy or distorted input data in order to estimate maximally discriminant directions. We demonstrate the efficiency of the proposed uncertain LDA on two applications using state-of-the-art techniques. First, we experiment with an automatic speech recognition task, in which the uncertainty of observations is imposed by real-world additive noise. Next, we examine a full-scale speaker recognition system, considering the utterance duration as the source of uncertainty in authenticating a speaker. The experimental results show that when employing an appropriate uncertainty estimation algorithm, uncertain LDA outperforms its conventional LDA counterpart.