A bayesian approach to the spectral F-Test: Application to auditory steady-state responses

Auditory steady-state responses (ASSRs) represent an objective method used in clinical practice to assess hearing thresholds. The steady-state nature of these signals allows response detection by means of statistical techniques in the frequency domain as spectral F-test. This objective response detection (ORD) compares the power of the response bin against the power of the neighboring frequency noise bins. Most ORD algorithms are based on the Neyman-Pearson approach to the hypothesis test provided that the likelihood ratio test is the most powerful test for a given significance level alpha (also called Type I error). On the other hand, the Bayesian approach allows the inclusion of prior information in the model and enables the updating of this information with posterior knowledge. This approach, however, has not been explored with respect to ORD techniques, thus enabling the exploration of new paradigms, which may contribute to this field of study, especially in terms of the time required for response detection. The aim of this study is to use the Bayesian approach in the implementation of the spectral F-test for application to ASSRs.

Monte Carlo simulations were performed to evaluate Neyman-Pearson and Bayesian detectors' performances with the spectral F-test as a function of the signal-to-noise ratio. Then, the two detectors were applied to ASSR recordings of nine normal-hearing individuals subjected to amplitude-modulated tones of various intensities.

Both simulation and ASSR data analyses showed that among the scenarios analyzed, the most promising case was that in which the lowest possible values for the a priori probability were selected for the null hypothesis (H0), allowing detection at low signal-to-noise ratios. The worst performance occurred when the a priori probabilities for both hypotheses were equal. The ASSR data also showed that higher stimulus intensity led to better performance and faster detection due to improvements in the signal-to-noise ratio.

The a priori probabilities can affect the Bayesian detector's performance, directly impacting the time needed to identify responses. The parallel behaviors observed between the performances of both approaches showed that the Bayesian detector can achieve its ideal performance at lower signal-to-noise ratios compared to the optimal performance of the Neyman-Pearson detector, reflecting the promising applicability of the Bayesian approach to evoked potentials.