Bayesian adaptive estimation of the auditory filter

Abstract

A Bayesian adaptive procedure for estimating the auditory-filter shape was proposed and evaluated using young, normal-hearing listeners at moderate stimulus levels. The resulting quick-auditory-filter (qAF) procedure assumed the power spectrum model of masking with the auditory-filter shape being modeled using a spectrally symmetric, two-parameter rounded-exponential (roex) function. During data collection using the qAF procedure, listeners detected the presence of a pure-tone signal presented in the spectral notch of a noise masker. Dependent on the listener's response on each trial, the posterior probability distributions of the model parameters were updated, and the resulting parameter estimates were then used to optimize the choice of stimulus parameters for the subsequent trials. Results showed that the qAF procedure gave similar parameter estimates to the traditional threshold-based procedure in many cases and was able to reasonably predict the masked signal thresholds. Additional measurements suggested that occasional failures of the qAF procedure to reliably converge could be a consequence of incorrect responses early in a qAF track. The addition of a parameter describing lapses of attention reduced the likelihood of such failures.

Figure 1

The results of 150 qAF trials are plotted for S1. The left panel shows the values of signal strength (x, upper) and notch bandwidth (Δf/f₀, lower) tested on each trial. The right panels indicate the estimated value of K, r, and p (top to bottom) following each trial.

Figure 2

A portion of the two-dimensional psychometric function estimated from the data of S1 is shown. Circles indicate locations in the signal-level × notch-bandwidth stimulus space visited by the qAF procedure. Larger circles indicate a larger number of trials at that point in the stimulus space.

Figure 3

(Color online) The posterior parameter distributions for the fourth qAF run for listener S1 (left) and the third qAF run for listener S4 (right). For the two runs shown here, the posterior distribution has been collapsed across the K, r, and p dimensions in the top, middle, and bottom panels, respectively. The dashed lines mark the 95% credibility limits for the model parameters based on their marginal distributions and the cross indicates the mean (which is also the parameter estimate).

Figure 4

Thresholds predicted based on the qAF model after 50 (unfilled circles) and 150 (filled circles) trials are plotted as a function of the observed thresholds. Only thresholds near or larger than 25 dB SPL were evaluated. The dashed line indicates equal estimates.

Figure 5

Estimates of ERBs are plotted for (left) S2 and (right) S4 for experiments (top) II and (bottom) IIIa as functions of the number of trials. The black symbols are for condition 1 and the gray symbols are for condition 5. The first and second runs are indicated using filled and unfilled symbols, respectively. The diamond in each panel indicates the corresponding ERB estimate obtained using the threshold-based procedure from experiment I.

Figure 6

Scatter plots of results for conditions 1 and 5 are plotted for (left) Group 1 and (right) Group 2 of experiment IIIb. The number of trials completed is indicated in the legends. The dashed line indicates equal estimates.