Acoustic mode frequencies in the Sun and Sun-like stars change due to magnetic activity, on time-scales much larger than the star's rotation and much smaller than its evolution. Given the poor S/N of the observed stellar p-modes, it is challenging to measure the changes of individual mode frequencies. Typically, power spectra of different time series segments are cross-correlated to estimate a mean p-mode frequency change, which ends up averaging over the individual mode contributions. We seek to enhance the cross-correlation method, by introducing a novel and computationally cheap method, thus enabling us to disentangle p-mode frequency changes for different spherical harmonic degree $\ell$. Assuming that the inclination angle and rotation rate are already measured, filters are designed, which enable the isolation of $δω_\ell$, frequency changes of modes with a given $\ell$, while preventing bias creeping in from neighbouring modes. Monte-Carlo simulations are performed to quantify uncertainty in the estimation of $δω_\ell$. We validate our method against well-studied solar data (SOHO/VIRGO and BiSON) and demonstrate its applicability to the solar-like Kepler star KIC 8006161.
Modern machine learning is leading to substantial gains in precision, flexibility, and computational efficiency in fundamental physics. Statistical validation, uncertainty quantification, and robustness assessment are less systematically addressed. The VERaiPHY initiative (Validation & Evaluation for Robust AI in PHYsics) is a series of articles developed within the PHYSTAT programme, aimed at establishing statistical standards for the development, evaluation, and deployment of ML techniques. Each article focuses on a specific methodological domain from a statistics perspective and clarifies statistical questions, tests, and the interpretation of results. This opening article establishes the probabilistic, statistical, and machine learning foundations that the later contributions assume, together with the notation used throughout.