2021MNRAS.501.2268W

Robust model-fitting to spectroscopic transitions is a requirement across many fields of science. The corrected Akaike and Bayesian information criteria (AICc and BIC) are most frequently used to select the optimal number of fitting parameters. In general, AICc modelling is thought to overfit (too many model parameters) and BIC underfits. For spectroscopic modelling, both AICc and BIC lack in two important respects: (a) no penalty distinction is made according to line strength such that parameters of weak lines close to the detection threshold are treated with equal importance as strong lines and (b) no account is taken of the way in which a narrow spectral line impacts only on a very small section of the overall data. In this paper, we introduce a new information criterion that addresses these shortcomings, the Spectral Information Criterion (SpIC). Spectral simulations are used to compare performances. The main findings are (i) SpIC clearly outperforms AICc for high signal-to-noise data, (ii) SpIC and AICc work equally well for lower signal-to-noise data, although SpIC achieves this with fewer parameters, and (iii) BIC does not perform well (for this application) and should be avoided. The new method should be of broader applicability (beyond spectroscopy), wherever different model parameters influence separated small ranges within a larger data set and/or have widely varying sensitivities.