Model selection for spectral parameterization

Abstract

Neurophysiological brain activity comprises rhythmic (periodic) and arrhythmic (aperiodic) signal elements, which are increasingly studied in relation to behavioral traits and clinical symptoms. Current methods for spectral parameterization of neural recordings rely on user-dependent parameter selection, which challenges the replicability and robustness of findings. Here, we introduce a principled approach to model selection, relying on Bayesian information criterion, for static and time-resolved spectral parameterization of neurophysiological data. We present extensive tests of the approach with ground-truth and empirical magnetoencephalography recordings. Data-driven model selection enhances both the specificity and sensitivity of spectral and spectrogram decompositions, even in non-stationary contexts. Overall, the proposed spectral decomposition with data-driven model selection minimizes the reliance on user expertise and subjective choices, enabling more robust, reproducible, and interpretable research findings.

Keywords: Magnetoencephalography; Model selection; Neurophysiology; Parameter optimization; Reproducibility in research; Rhythmic and arrhythmic brain signals; Spectral decomposition; Time-frequency analysis.

Figure 1:. Spectral Parameterization with Model Selection

(a) Illustration of a spectral parameterization of a simulated power spectral density estimate (black line) obtained with specparam in the context of lower (left panel) and higher (right panel) noise levels. Both spectra are generated using the same spectral parameters (i.e., two spectral peaks). In more noisy conditions, specparam (pink line) fits a greater number of spectral peaks (green shaded areas) than what is present (simulated) in the data, resulting in overfitting (right panel). Key: ‘cf’ refers to a peak’s center frequency, ‘amp’ refers to a peak’s amplitude, and ‘bw’ refers to a peak’s bandwidth. (b) ms-specparam is a method for spectral parameterization combined with a model selection procedure. It first adjusts a model for the aperiodic component of the spectrum (subpanel i) before adding spectral peaks (green shaded areas) in an iterative fashion (subpanel ii). These successive models are then assessed via the Bayesian Information Criterion (BIC; subpanel iii). (c) The resulting BIC model is then subjected to Bayes factor inference against the aperiodic spectral model (panel i) to adjudicate whether spectral peaks are likely to be present in the data power spectrum. A Bayes factor greater than 1 is evidence in favour of periodic brain activity over the null hypothesis of no periodic activity (panel iv).

Figure 2:. Performances on Synthetic Stationary Data

(a) Sensitivity and positive predictive value (PPV) for detection of spectral peaks (top row). ms-specparam (green) has similar sensitivity (89%) than default-specparam (blue; 91%), but superior PPV (96% vs. 63%). The heat maps below report the ground-truth vs. estimated number of spectral peaks (with percent incidence listed in each element) and highlight ms-specparam’s improved peak detection accuracy. (b) Boxplots and empirical density distributions reporting the errors on the estimates of the spectral parameters derived using ms-specparam and default-specparam. For every spectral parameter, ms-specparam estimated values with significantly lower mean absolute error (one-tailed permutation t-test, all p<0.05).

Figure 3:. Performances on Synthetic Data with Time-Varying Spectral Contents

(a) Heat maps reporting the number of spectral peaks detected vs. ground-truth. ms-SPRiNT with post-processing (purple; bottom right) best recovers the true number of spectral peaks. Numbers of datasets synthesized with 0 spectral peaks = 798,753, 1 peak = 256,599, 2 peaks = 78,698, 3 peaks = 14,790, and 4 peaks = 1160. (b) Sensitivity of spectral peak detection (N = 10,000 simulated time series). ms-SPRiNT with (purple) and without post-processing (fuchsia) exhibit marginally lower sensitivity than the default SPRiNT algorithm (orange). (c) Positive predictive value (PPV) of spectral peak detection. ms-SPRiNT with post-processing (purple) exhibits a higher positive predictive value than all other algorithms.

Figure 4:. Performances on Empirical MEG Data

(a) Residual variance analysis across the 606 participants and all brain regions shows ms-specparam (green) with consistently lower residual variance, indicating a superior fit relative to the other spectral parameterization methods (blue and yellow; left panel). The brain maps display residual variance values for each cortical parcel. A frequency breakdown (right panel) reveals ms-specparam outperforms the other two tested specparam variations across the spectrum, particularly at the edges of the frequency spectrum. (b) ms-specparam estimates less spectral peaks than default-specparam, demonstrating more parsimonious modeling, as reported in the box/density plots (left panel). The brain maps indicate that less spectral peaks were detected in posterior cortical parcels with ms-specparam (right panel). (c) Bayesian evidence for periodic, rhythmic brain activity mapped across the cortical surface emphasizes occipital and left temporal regions. (d) Parameterized spectra from the right post-central gyrus of a sample subject highlight the differences between algorithms: ms-specparam fits two peaks (right panel), reflecting the dominant oscillations, whereas default-specparam fits five (left panel), some of which may be redundant or overfitted, as seen in the overlaid spectral models.

Figure 5:. Age-related Neural Spectral Changes and Algorithmic Parsimony

(a) Topographical differences in aperiodic neural components, showing the variations in exponent (top) and offset (bottom) estimates when using ms-specparam versus default-specparam. Areas where ms-specparam yields higher parameter estimates are highlighted in blue. (b) Moderating effect of spectral parameterization method (ms-specparam vs. Default-specparam) on the relationship between age and aperiodic spectral components. The left graph shows the exponent, and the right graph displays the offset, with statistical interactions highlighted. (c) Frequency-specific empirical distribution of the number of peaks fitted across different age groups. The histograms show that ms-specparam (green) generally fits fewer peaks, especially in the mid-frequency range (8–30Hz), illustrating a more parsimonious approach to model fitting and potentially more accurate reflection of age-related spectral changes.