Robust and efficient Bayesian adaptive psychometric function estimation

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.

Optimised adaptive procedures and analysis methods for conducting speech-in-noise tests

OBJECTIVE

Speech-in-noise testing is a valuable part of audiological test batteries. Test standardisation using precise methods is desirable for ease of administration. This study investigated the accuracy and reliability of different Bayesian and non-Bayesian adaptive procedures and analysis methods for conducting speech-in-noise testing.

DESIGN

Matrix sentence tests using different numbers of sentences (10, 20, 30 and 50) and target intelligibilities (50 and 75%) were simulated for modelled listeners with various characteristics. The accuracy and reliability of seven different measurement procedures and three different data analysis methods were assessed.

RESULTS

The estimation of 50% intelligibility was accurate and showed excellent reliability across the majority of methods tested, even with relatively few stimuli. Estimating 75% intelligibility resulted in decreased accuracy. For this target, more stimuli were required for sufficient accuracy and selected Bayesian procedures surpassed the performance of others. Some Bayesian procedures were also superior in the estimation of psychometric function width.

CONCLUSIONS

A single standardised procedure could improve the consistency of the matrix sentence test across a range of target intelligibilities. Candidate adaptive procedures and analysis methods are discussed. These could also be applicable for other speech materials. Further testing with human participants is required.

Bayesian Adaptive Estimation with Theoretical Bound: An Exploration-Exploitation Approach

This paper investigates the theoretical bound to reduce the parameter uncertainty in Bayesian adaptive estimation for psychometric functions and proposes an exploration-exploitation (E-E) approach to improve the computation efficiency for parameter estimations. When the experimental trial goes on, the uncertainty of the parameters decreases dramatically and the space between the maximal mutual information and the theoretical bound gets narrower, so the advantage of classical Bayesian adaptive estimation algorithm diminishes. This approach tries to trade off the exploration (parameter posterior uncertainty) and the exploitation (parameter mean estimation). The experimental results show that the proposed E-E approach estimates parameters for psychometric functions with same convergence and reduces the computation time by more than 34.27%, compared with the classical Bayesian adaptive estimation.

The one-up one-down adaptive (staircase) procedure in speech-in-noise testing: Standard error of measurement and fluctuations in the track

The one-up one-down adaptive (staircase or up-down) procedure is often used to estimate the speech recognition threshold (SRT) in speech-in-noise testing. This article provides a brief historical overview of the one-up one-down procedure in psychophysics, discussing the groundbreaking early work that is still relevant to clinical audiology and scientific research. Next, this article focuses on two aspects of the one-up one-down adaptive procedure: first, the standard error of measurement (SEM) and, second, the fluctuations in the track [i.e., the standard deviation of the signal-to-noise ratios of the stimuli within the track (SD_track)]. Simulations of ideal and non-ideal listeners and experimental data are used to determine and evaluate different relationships between the parameters slope of the speech recognition function, SRT, SEM, and SD_track. Hearing loss and non-ideal behavior (inattentiveness, fatigue, and giving up when the task becomes too difficult) slightly increase the average value of SD_track. SD_track, however, poorly discriminates between reliable and unreliable SRT estimates.

Efficient Adaptive Speech Reception Threshold Measurements Using Stochastic Approximation Algorithms

This study examines whether speech-in-noise tests that use adaptive procedures to assess a speech reception threshold in noise (SRT50n) can be optimized using stochastic approximation (SA) methods, especially in cochlear-implant (CI) users. A simulation model was developed that simulates intelligibility scores for words from sentences in noise for both CI users and normal-hearing (NH) listeners. The model was used in Monte Carlo simulations. Four different SA algorithms were optimized for use in both groups and compared with clinically used adaptive procedures. The simulation model proved to be valid, as its results agreed very well with existing experimental data. The four optimized SA algorithms all provided an efficient estimation of the SRT50n. They were equally accurate and produced smaller standard deviations (SDs) than the clinical procedures. In CI users, SRT50n estimates had a small bias and larger SDs than in NH listeners. At least 20 sentences per condition and an initial signal-to-noise ratio below the real SRT50n were required to ensure sufficient reliability. In CI users, bias and SD became unacceptably large for a maximum speech intelligibility score in quiet below 70%. In conclusion, SA algorithms with word scoring in adaptive speech-in-noise tests are applicable to various listeners, from CI users to NH listeners. In CI users, they lead to efficient estimation of the SRT50n as long as speech intelligibility in quiet is greater than 70%. SA procedures can be considered as a valid, more efficient, and alternative to clinical adaptive procedures currently used in CI users.

Application of Bayesian Active Learning to the Estimation of Auditory Filter Shapes Using the Notched-Noise Method

Time-efficient hearing tests are important in both clinical practice and research studies. This particularly applies to notched-noise tests, which are rarely done in clinical practice because of the time required. Auditory-filter shapes derived from notched-noise data may be useful for diagnosis of the cause of hearing loss and for fitting of hearing aids, especially if measured over a wide range of center frequencies. To reduce the testing time, we applied Bayesian active learning (BAL) to the notched-noise test, picking the most informative stimulus parameters for each trial based on nine Gaussian Processes. A total of 11 hearing-impaired subjects were tested. In 20 to 30 min, the test provided estimates of signal threshold as a continuous function of frequency from 500 to 4000 Hz for nine notch widths and for notches placed both symmetrically and asymmetrically around the signal frequency. The thresholds were found to be consistent with those obtained using a 2-up/1-down forced-choice procedure at a single center frequency. In particular, differences in threshold between the methods did not vary with notch width. An independent second run of the BAL test for one notch width showed that it is reliable. The data derived from the BAL test were used to estimate auditory-filter width and asymmetry and detection efficiency for center frequencies from 500 to 4000 Hz. The results agreed with expectations for cochlear hearing losses that were derived from the audiogram and a hearing model.

Bayesian active probabilistic classification for psychometric field estimation

Psychometric functions are typically estimated by fitting a parametric model to categorical subject responses. Procedures to estimate unidimensional psychometric functions (i.e., psychometric curves) have been subjected to the most research, with modern adaptive methods capable of quickly obtaining accurate estimates. These capabilities have been extended to some multidimensional psychometric functions (i.e., psychometric fields) that are easily parameterizable, but flexible procedures for general psychometric field estimation are lacking. This study introduces a nonparametric Bayesian psychometric field estimator operating on subject queries sequentially selected to improve the estimate in some targeted way. This estimator implements probabilistic classification using Gaussian processes trained by active learning. The accuracy and efficiency of two different actively sampled estimators were compared to two non-actively sampled estimators for simulations of one of the simplest psychometric fields in common use: the pure-tone audiogram. The actively sampled methods achieved estimate accuracy equivalent to the non-actively sampled methods with fewer observations. This trend held for a variety of audiogram phenotypes representative of the range of human auditory perception. Gaussian process classification is a general estimation procedure capable of extending to multiple input variables and response classes. Its success with a two-dimensional psychometric field informed by binary subject responses holds great promise for extension to complex perceptual models currently inaccessible to practical estimation.

Feasibility of interleaved Bayesian adaptive procedures in estimating the equal-loudness contour

A Bayesian adaptive procedure, the interleaved-equal-loudness contour (IELC) procedure, was developed to improve the efficiency in estimating the equal-loudness contour. Experiment 1 evaluated the test-retest reliability of the IELC procedure using six naive normal-hearing listeners. Two IELC runs of 200 trials were conducted and excellent test-retest reliability was found at both the group and individual levels. Using the same group of listeners, Experiment 2 compared the IELC procedure to two other procedures that required frequency-by-frequency testing. One of these procedures was the commonly adopted interleaved staircase (ISC) procedure from Jesteadt [(1980). Atten. Percept. Psychophys. 28, 85-88]. The other procedure, the interleaved maximum-likelihood (IML) procedure, was a modification of the updated maximum-likelihood procedure [Shen and Richards (2012). J. Acoust. Soc. Am. 132, 957-967]. For each of the ISC and IML procedures, two runs of approximately 500 trials were conducted, followed by one additional IELC run. The test-retest reliability of the IELC procedure was comparable to that of the ISC and IML procedure. The accuracies of all three procedures measured in Experiment 2 were similar, which was superior to the accuracies of the IELC runs from Experiment 1, indicating a potential training effect.