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Laurence T. Maloney, Pascal Mamassian; The visual system uses different estimators for different distributions in a novel task even without feedback or the possibility of learning. Journal of Vision 2008;8(6):74. doi: https://doi.org/10.1167/8.6.74.
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© ARVO (1962-2015); The Authors (2016-present)
Purpose. Bayesian decision theory (BDT) is often used as a model of visual processing with the assumption that visual uncertainty is Gaussian and that estimators minimize variance (MV) or maximize posterior probability (MAP). BDT applies equally well to other distributional families and the resulting MV and MAP estimators can be very different from that appropriate for the Gaussian. Our goal is to examine whether the visual system has the same facility in selecting optimal estimators when the distribution family is not Gaussian. Methods. We selected two distributional families, the circular Gaussian and the Uniform on a circular arc. Samples were presented as points on an invisible circle centered on fixation. The distributions were equated for variance and the true center of each distribution was distributed uniformly on the circle from trial to trial. In an initial training phase, eleven naïve participants were trained to discriminate the distributions (identified only as “A” and “B”). Eight participants with estimated d'[[gt]]1 continued on to the second, estimation phase. They were told that a block of 300 trials contained samples of size 9 drawn from the now familiar A (or B) distribution and asked to estimate the center of the (invisible) distribution by adjusting a circular cursor. No feedback occurred. They then repeated this task for the other distribution. Prior training ensured that participants understood the task. Analysis. We characterized both MV/MAP estimators and observers' performance by the weight assigned to each point when the sample is ordered. We could then compare them. Results. Participants deviated significantly from MV/MAP in judging both distributions, but they spontaneously selected different estimators for each distribution. The difference between the pattern of weights for the two distributions was qualitatively correct. The visual system uses different estimators even without feedback or the possibility of learning.
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