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Syaheed B. Jabar, Daryl Fougnie; How complex can the 'shape' of expectations be? Investigating error distributions under skewed priors.. Journal of Vision 2020;20(11):286. doi: https://doi.org/10.1167/jov.20.11.286.
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© ARVO (1962-2015); The Authors (2016-present)
The visual world is full of statistical regularities; stop signs are red and bananas usually are yellow. While such regularities can be quite complex, we tend to study priors that consist of Gaussian distributions. Research has shown that participants are sensitive to the mean and variance of distributions. Here we explore whether people can adapt to more complex distributions, i.e. with skew. To investigate this, we employed a delayed color-matching task where the shape of a trial-by-trial prior (expectation) was visually made available at response. The prior was either symmetrically distributed or had (positive/ negative) skew. Bayesian-like effects (bias towards the prior and reduced error) were observed, suggesting integration of priors. Multiple pieces of evidence point to participants being sensitive to skew. Although unintuitive, Bayesian observer models predict that positively-skewed priors result in negatively-skewed error distributions (and vice-versa), which we observed, (t(20) = 3.43, p = .003). This skew flip was replicated with a task requiring multiple responses (t(20) = 2.34, p = .030), and when priors were fixed across blocks, (t(20) = 2.39, p = .027). Model fits further suggested that 45 out of 63 participants were more likely to have used the skew information, versus approximating the priors as Gaussians. To demonstrate this behaviorally, we compared providing additional participants (n = 21) with a skewed prior versus the best Gaussian approximation of that prior. Kolmogorov-Smirnov tests suggested that the shape of the communicated prior led to significantly different error distributions (D = .065, p < .001) even though the stimulus distributions were equivalent. These results show that people are sensitive to more than expected mean, mode, and variance of stimuli in the environment; people can encode and utilize information about third-order statistics such as skew. This work is further evidence that perception is richly sensitive to stimulus probabilities.
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