Hierarchical Bayesian augmented Hebbian reweighting model of perceptual learning

The augmented Hebbian reweighting model (AHRM) has proven effective in modeling the collective performance of observers in perceptual learning studies. In this work, we introduce a novel hierarchical Bayesian version of the AHRM (HB-AHRM), which allows us to model the learning curves of individual participants and the entire population within a unified framework. We compare the performance of HB-AHRM with that of a Bayesian inference procedure, which independently estimates posterior distributions of model parameters for each participant without using a hierarchical structure. To address the substantial computational challenges, we propose a method for approximating the likelihood function in the AHRM through feature engineering and linear regression, increasing the speed of the estimation process by a factor of 20,000. This enhancement enables the HB-AHRM to compute the posterior distributions of hyperparameters and model parameters at the population, subject, and test levels, facilitating statistical inferences across these layers. Although developed in the context of a single experiment, the HB-AHRM and its associated methods are broadly applicable to data from various perceptual learning studies, offering predictions of human performance at both individual and population levels. Furthermore, the approximated likelihood approach may prove useful in fitting other stochastic models that lack analytic solutions.