Toward parametric Bayesian adaptive procedures for multi-frequency categorical loudness scaling

A series of Bayesian adaptive procedures to estimate loudness growth across a wide frequency range from individual listeners was developed, and these procedures were compared. Simulation experiments were conducted based on multinomial psychometric functions for categorical loudness scaling across ten test frequencies estimated from 61 listeners with normal hearing and 87 listeners with sensorineural hearing loss. Adaptive procedures that optimized the stimulus selection based on the interim estimates of two types of category-boundary models were tested. The first type of model was a phenomenological model of category boundaries adopted from previous research studies, while the other type was a data-driven model derived from a previously collected set of categorical loudness scaling data. An adaptive procedure without Bayesian active learning was also implemented. Results showed that all adaptive procedures provided convergent estimates of the loudness category boundaries and equal-loudness contours between 250 and 8000 Hz. Performing post hoc model fitting, using the data-driven model, on the collected data led to satisfactory accuracies, such that all adaptive procedures tested in the current study, independent of modeling approach and stimulus-selection rules, were able to provide estimates of the equal-loudness-level contours between 20 and 100 phons with root-mean-square errors typically under 6 dB after 100 trials.