ABSTRACT We develop an automatic peak fitting algorithm using the Bayesian information criterion (BIC) fitting method with confidence-interval estimation in spectral decomposition. First, spectral decomposition is carried out by adopting the Bayesian exchange Monte Carlo method for various artificial spectral data, and the confidence interval of fitting parameters is evaluated. From the results, an approximated model formula that expresses the confidence interval of parameters and the relationship between the peak-to-peak distance and the signal-to-noise ratio is derived. Next, for real spectral data, we compare the confidence interval of each peak parameter obtained using the Bayesian exchange Monte Carlo method with the confidence interval obtained from the BIC-fitting with the model selection function and the proposed approximated formula. We thus confirm that the parameter confidence intervals obtained using the two methods agree well. It is therefore possible to not only simply estimate the appropriate number of peaks by BIC-fitting but also obtain the confidence interval of fitting parameters.

中文翻译：

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基于具有置信区间估计的贝叶斯信息准则的谱分解的发展

摘要 我们使用贝叶斯信息准则 (BIC) 拟合方法开发了一种自动峰值拟合算法，在频谱分解中具有置信区间估计。首先，对各种人工光谱数据采用贝叶斯交换蒙特卡罗方法进行光谱分解，评估拟合参数的置信区间。根据结果​​，推导出一个近似的模型公式，该公式表示参数的置信区间以及峰峰距离与信噪比之间的关系。接下来，对于真实的光谱数据，我们将使用贝叶斯交换蒙特卡罗方法获得的每个峰值参数的置信区间与使用模型选择函数和建议的近似公式通过 BIC 拟合获得的置信区间进行比较。因此，我们确认使用两种方法获得的参数置信区间吻合良好。因此，不仅可以通过 BIC 拟合简单地估计适当的峰值数量，而且还可以获得拟合参数的置信区间。