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Mikhail Katkov, Tal Gan, Misha Tsodyks, Dov Sagi; Singularities in the inverse modeling of contrast discrimination and ways to avoid them. Journal of Vision 2005;5(8):455. doi: 10.1167/5.8.455.
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© ARVO (1962-2015); The Authors (2016-present)
A basic problem in psychophysics is estimating the mean internal response and noise amplitude from sensory discrimination data. However, these components cannot be measured independently and therefore several indirect methods were suggested to resolve this issue. Here we analyze the two-alternative forced-choice method (2AFC), using a signal detection theory approach, and show analytically that some combinations of internal parameters exhibit singularities in the sensitivity to sampling errors, which results in a large range of estimated parameters with a finite number of experimental trials. Four types of singularities were identified. It was found that performances, measured as percent correct discriminations in 2AFC contrast discrimination experiments, are well described by a model with the noise amplitude that is independent of the stimulus intensity (one of the singular models). Thus, the 2AFC contrast discrimination experiment is not suitable for characterization of the contrast perception model. We show that this problem can be avoided using a visual category rating task, with Gabor signals at nine contrast levels as targets. Assuming stable category boundaries, the model parameters, namely, mean internal responses, noise amplitudes and category boundaries were found using a best least square fit to the data. Our findings show that at low contrasts noise amplitude decreases as a function of contrast level, while at higher contrasts the amplitude is independent of the contrast level. The internal responses were found to be best described by a saturating function of contrast. The confidence intervals were estimated using Monte-Carlo simulations of the identification task. The results show that the well-known increase of contrast discrimination thresholds with contrast is due to reduced sensory gain and not due to increasing internal noise.
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