Getting the model right; an information criterion for spectroscopy
  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 spectral lines impact on narrow data regions. 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 dataset and/or have widely varying sensitivities.
