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Alan A. Stocker, Eero P. Simoncelli; Constraining the prior and likelihood in a Bayesian model of human visual speed perception. Journal of Vision 2005;5(8):928. doi: 10.1167/5.8.928.
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© ARVO (1962-2015); The Authors (2016-present)
The perceived visual speed of a translating spatial intensity pattern varies as a function of stimulus contrast, and is qualitatively consistent with that predicted by an optimal Bayesian estimator based on a Gaussian prior probability distribution that favors slow speeds (Weiss, Simoncelli & Adelson, 2002). In order to validate and further refine this hypothesis, we have developed a more general version of the model. Specifically, we assume the estimator computes velocity from internal measurements corrupted by internal noise whose variance can depend on both stimulus speed and contrast. Furthermore, we allow the prior probability distribution over speed to take on an arbitrary shape. Using classical signal detection theory, we derive a direct relationship between the model parameters (the noise variance, and the shape of the prior) and single trial data obtained in a two-alternative forced choice speed-discrimination task. We have collected psychophysical data, in which subjects were asked to compare the apparent speeds of paired patches of drifting gratings differing in contrast and/or speed. The experiments were performed over a large range of perceptually relevant contrast and speed values. Local parametric fits to the data reveal that the likelihood function is well approximated by a Normal distribution in the log speed domain, with a variance that depends only on contrast. The prior distribution on speed that best accounts for the data shows significantly heavier tails than a Gaussian, and can be well approximated across all subjects by a power-law function with an exponent of 1.4. We describe a potential neural implementation of this model that matches the derived forms of the likelihood and prior functions.
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