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Luis A. Lesmes, Simon Jeon, Zhong-Lin Lu, Barbara A. Dosher; Bayesian adaptive estimation of threshold versus external noise contrast functions. Journal of Vision 2005;5(8):458. doi: https://doi.org/10.1167/5.8.458.
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© ARVO (1962-2015); The Authors (2016-present)
Purpose. Contrast threshold as a function of external noise contrast (the TvC function), measured at multiple performance criterion levels, provides a fundamental description of the observer system that distinguishes mechanisms of adaptation, spatial attention, and perceptual learning. Previously, measuring TvC functions at three criterion levels, required for model inference, has been demanding (often>2000 trials). We develop and test a Bayesian adaptive procedure to estimate multiple TvCs with 240–480 trials. Method. Based on Kontsevich and Tyler's Ψ method, the quick TvC (qTvC) procedure estimates three parameters: c0 and N determine a bilinear approximation to the TvC at 79% correct— c0 determines the constant threshold level observed in low noise and N determines the noise level at which thresholds begin increasing with slope=1.0. The third parameter,γ, determines the constant threshold ratio between criterion levels across noise conditions. This slope invariance assumption (validated by dozens of data sets) allows us to estimate TvCs at other criterion levels (e.g.,65,92%). On each trial, stimuli are placed at signal and noise contrast levels minimizing the entropy of the three-dimensional posterior probability distribution, p(c0,N,γ) in a one-step ahead search. The procedure was tested in Monte Carlo simulations and a psychophysical task comparing qTvC estimates (240–480 trials) with those obtained using constant stimuli (1920 trials). Results. Simulations showed that after 240 and 480 trials, the rms error of qTvC estimates at three criterion levels is 1.3 and .9 dB. Further, qTvC and constant stimulus estimates were very similar: the rms difference was .9±1.1 dB. Conclusions. The qTvC method holds considerable practical value: it measures the observer system's functional properties (equivalent internal noises corresponding to absolute threshold and Weber fraction),within a plausible data collection regime for special populations or testing applications.
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