Measuring response bias from a confusion matrix Given a confusion matrix of a binary classifier, what are the best measures of response bias towards one of the classes?
One idea that comes to mind is Signal Detection Theory's criterion, but this measure assumes a Gaussian noise model.
Is there a more straightforward, well-tested measure of response bias? For example, we could divide the number of predicted positives (TP + FP) by the number of positives (TP + FN), but I'm not sure that such a ratio would be "well behaved".

The Python package sdt_metrics by Roger Lew implements several non-parametric response bias measures. Unfortunately, the package is not maintained, but the references are still useful.
One of these references is an empirical study comparing five response bias measures:

See, J. E., Warm, J. S., Dember, W. N., and Howe, S. R. (1997).
Vigilance and signal detection theory: An empirical evaluation of five
measures of response bias. https://doi.org/10.1518/001872097778940704

Among the parametric response bias measures, they recommend B"D:
$$B’’_D = \frac{(1-H)(1-FA)-(H)(FA)}{(1-H)(1-FA)+(H)(FA)}$$
Note that care must be taken when $H$ (hit rate) or $FA$ (false alarm rate) are at their boundaries:

Hautus, M.J. Corrections for extreme proportions and their biasing
effects on estimated values of d′. Behavior Research Methods,
Instruments, & Computers 27, 46–51 (1995).
https://doi.org/10.3758/BF03203619

