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Keiji Ota, Qihan Wu, Pascal Mamassian, Laurence Maloney; Visual cue estimation with non-gaussian distribution. Journal of Vision 2020;20(11):1436. doi: https://doi.org/10.1167/jov.20.11.1436.
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Introduction. Many models of ideal perception and action presuppose that error probability density functions are Gaussian. In cue combination (Landy et al., 1995), ideal combination results in a combined estimate that is unbiased and that minimizes variance (UMVUE) but only if the underlying distributions are Gaussian (Oruc et al., 2003). What if the distributions were not Gaussian? Are we just Gaussian machines or do we have a wider range of adaptability to scene statistics? Would the visual system continue to employ the sub-optimal Gaussian rule? Or would it adapt to the UMVUE of a new distribution? To investigate this hypothesis, we asked observers to estimate the population mean of samples drawn from a Gaussian, Laplacian, or Uniform distribution. The UMVUE for the Gaussian is the mean of the sample, for the Laplacian, it is the median, and for the Uniform it is the average of the largest and smallest value. Methods. Twenty observers saw 9 dots and had to locate the mean of the underlying distribution. They received initial training with the three distributions/samples interleaved. The samples were color-coded so that the observer always knew which distribution a sample came from. Analysis. We performed a regression analysis to estimate the observer’s weights on sample information and compared it with normative UMVUE weights. Observers markedly changed their weights for three different samples. For a uniform sample, they correctly used the average of the two bounds of the sample. For a Laplacian sample, the observers relied mostly on the points around the median. Interestingly, the rule used for the Gaussian was not UMVUE but distinct from that used for either of the other distributions. Learning the new rules took less than 100 trials. Conclusion. Human estimates were not perfect, but humans use of sample information varied with the underlying distribution.
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