Getting the model right; an information criterion for spectroscopy

TL;DR

This paper introduces the Spectral Information Criterion (SpIC), a new model selection method for spectroscopy that improves over AICc and BIC by accounting for line strength and local data impact, especially at high signal-to-noise ratios.

Contribution

The paper presents SpIC, a novel information criterion tailored for spectroscopic data, addressing limitations of existing criteria by incorporating line strength and local spectral effects.

Findings

SpIC outperforms AICc at high signal-to-noise ratios.

SpIC achieves similar results to AICc at lower noise with fewer parameters.

BIC performs poorly and should be avoided in this context.

Abstract

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.