建立正确的模型; spectroscopy的信息准则
Getting the model right; an information criterion for spectroscopy
摘要：
光谱跃迁的稳健模型拟合是许多科学领域的要求。修正赤池和贝叶斯信息准则（AICc和BIC）最常用于选择拟合参数的最佳数量。一般来说，AICc建模被认为是过拟合（太多的模型参数）和BIC欠拟合。对于光谱建模，AICc和BIC都缺乏两个重要方面：（a）没有根据谱线强度进行惩罚区分，使得接近检测阈值的弱谱线的参数与强谱线一样重要，以及（b）没有考虑谱线影响窄数据区域的方式。在本文中，我们介绍了一种新的信息标准，解决这些缺点，“光谱信息标准”（SpIC）。频谱模拟用于比较性能。主要发现是（i）SpIC在高信噪比数据方面明显优于AICc，（ii）SpIC和AICc在低信噪比数据方面同样有效，尽管SpIC使用较少的参数实现了这一点，以及（iii）BIC表现不佳（对于此应用），应避免使用。新方法应具有更广泛的适用性（超越光谱学），只要不同的模型参数影响较大数据集内的分离小范围和/或具有广泛变化的灵敏度。
英文摘要：
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.
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