Christian Canedo

Electroencephalographic (EEG) recordings often exhibit strong interchannel correlations due to scalp potentials reflecting electric fields generated by localized neural sources commonly modeled as current dipoles. Despite this physiological basis, many widely used approaches (e.g., independent component analysis) are largely data-driven, may require many components, and offer limited interpretability and limited support for assessing physiological assumptions. We propose a physiologically guided multichannel model built on a parametric Frequency-Modulated Möbius (FMM) formulation, where each electrode signal is expressed as a linear combination of a small number of latent dipole-related sources with parametrically described trajectories. The resulting framework captures temporal and spatial structure with high accuracy and enables likelihood-based testing of the fixed dipole-orientation assumption through a reduced-rank formulation. Using publicly available EEG data, we illustrate that the proposed approach explains interchannel dependence with few latent sources and provides statistical evidence regarding the plausibility of fixed orientation.

The Frequency Modulated Möbius (FMM) approach is a contemporary and versatile tool for analyzing oscillatory signals. Within the functional data analysis framework, the FMM model offers an accurate alternative for comprehending multidimensional synchronized oscillatory signals, which are common in various fields including biology and medicine. This approach decomposes the signals into scaled Möbius waves formulated in terms of four parameters, interpreted as measures of location and shape variation. Among these parameters, two are specific to individual signals, while the remaining two are global and describe the interconnections between signals. In this paper we extend the utility of the FMM by developing inferential procedures based on likelihood estimations for nonlinear models. These procedures cover the core parameters, the signals themselves, and their derivatives. We explore various techniques, including the Gauss–Seidel approach and profile likelihood, for obtaining estimators and their asymptotic properties. Our methodology undergoes rigorous validation, drawing on a combination of theoretical insights and numerical experiments. Furthermore, as our research is primarily motivated by the analysis of biomedical oscillatory signals, we apply this methodology to address two pertinent real-world problems involving electrocardiogram and pattern-reversal visual evoked potential data. These applications illustrate the practical efficacy of the new paradigm.