Threshold tests have recently been proposed as a useful method for detecting bias in lending, hiring, and policing decisions. For example, in the case of credit extensions, these tests aim to estimate the bar for granting loans to white and minority applicants, with a higher inferred threshold for minorities indicative of discrimination. This technique, however, requires fitting a complex Bayesian latent variable model for which inference is often computationally challenging. Here we develop a method for fitting threshold tests that is two orders of magnitude faster than the existing approach, reducing computation from hours to minutes. To achieve these performance gains, we introduce and analyze a flexible family of probability distributions on the interval [0, 1] -- which we call discriminant distributions -- that is computationally efficient to work with. We demonstrate our technique by analyzing 2.7 million police stops of pedestrians in New York City.
Psychophysical studies suggest the existence of specialized detectors for component motion patterns (radial, circular, and spiral), that are consistent with the visual motion properties of cells in the dorsal medial superior temporal area (MSTd) of nonhuman primates. Here we use a biologically constrained model of visual motion processing in MSTd, in conjunction with psychophysical performance on two motion pattern tasks, to elucidate the computational mechanisms associated with the processing of widefield motionpatterns encountered during self-motion. In both tasks discrimination thresholds varied significantly with the type of motion pattern presented, suggesting perceptual correlates to the preferred motion bias reported in MSTd. Through the model we demonstrate that while independently responding motion pattern units are capable of encoding information relevant to the visual motion tasks, equivalent psychophysical performance can only be achieved using interconnected neural populations that systematically inhibit non-responsive units. These results suggest the cyclic trends in psychophysical performance may be mediated, in part, by recurrent connections within motion pattern responsive areas whose structure is a function of the similarity in preferred motion patterns and receptive field locations between units.