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Yukai Zhao, Jiajuan Liu, Barbara Anne Dosher, Zhong-Lin Lu; Hierarchical Bayesian modeling of training accuracy and feedback interaction in perceptual learning. Journal of Vision 2021;21(9):2214. doi: https://doi.org/10.1167/jov.21.9.2214.
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Based on an analysis of the block-by-block learning curves, Liu et al. (2010) found that, although it was not necessary for perceptual learning at a high training accuracy, feedback was critical at a low training accuracy in a Gabor orientation identification task. In this study, we developed a hierarchical Bayesian model (HBM) to analyze the trial-by-trial data in Liu et al. (2010) to estimate the joint posterior distributions of the parameters and hyperparameters of the learning curves as well as their covariances at both the subject and group levels. The learning curves were modeled as exponential functions with three parameters: initial and asymptotic thresholds, and time constant (TC). We used the posterior distributions of the hyperparameters to compute the distributions of the mean (M) learning parameters as well as threshold-reduction learning effects (d’= M/SD) at the group level. Based on the 95% confidence interval of the d' distributions, we found significant perceptual learning in the low training accuracy with feedback (0.15±0.06 log10 units; d': 3.2±1.40; TC: 372±84 trials), high training accuracy with (0.20±0.04 log10 units; d': 6.1±2.23; TC: 364±70 trials) and without feedback (0.11±0.05 log10 units; d': 3.3±1.46; TC: 366±83 trials) conditions, but no significant learning in the low training accuracy condition (0.02±0.06 log10 units; d': 0.4±1.45). In addition, the magnitudes of learning and time constant were not significantly different among the three conditions that led to significant learning. Although the pattern of results was qualitatively the same as Liu et al. (2010), the trial-by-trial HBM model allowed us to quantify both individual observer and group variability in the full dataset in one unified model, characterizing the general properties of the learning curves at both levels simultaneously. The model also produces posterior distributions on parameters in all groups that can be used as priors for future Bayesian analyses.
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