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.