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Figure 1: Bayes-optimal classification error probability $e_{b}$ and Bayes discriminability index $d'_{b}$ between two univariate histograms computed from their overlap area. Figure 2: Same computed from the overlap volume of two bivariate histograms. Figure 3: discriminability indices of two univariate normal distributions with unequal variances. The classification boundary is in black. Figure 4: discriminability indices of two bivariate normal distributions with unequal covariance matrices (ellipses are 1 sd error ellipses). Color-bar shows the relative contribution to the discriminability by each dimension. These are computed by numerical methods^[1].

The sensitivity index or discriminability index or detectability index is a dimensionless statistic used in signal detection theory. A higher index indicates that the signal can be more readily detected.

^ Das, Abhranil; Wilson S Geisler (2020). "Methods to integrate multinormals and compute classification measures". arXiv:2012.14331 [stat.ML].

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