Detailed comparisons between theory and experiment for quantum electrodynamics (QED) effects in He-like ions have been performed in the literature to search for hints of new physics. Different frequentist statistical analyses of the existing atomic transition energy data have shown contradictory conclusions as to the presence of possible deviations from the theory predictions. We present here an approach using Bayesian statistics to assign quantitative probabilities to the different deviation models from theory for He-like ions for $Z=5–92$. Potential deviations beyond the standard model or higher-order QED effects are modeled with $f\left(Z\right)\propto Z^k$ functions. Considering the currently available data, no significant difference between theory and experiment is found, and we show that recent experiments have reduced the possible deviations previously observed in the literature. Using past measurements and a weighted average on the different deviation models, we estimate the accuracy required for future measurements to investigate possible anomalies.

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• Electronic transitions
• Fine & hyperfine structure
• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions