Title: On the analysis of signal peaks in pulse-height spectra Show Chinese title

Title: 脉冲幅度谱中信号峰的分析

Abstract: The estimation of the signal location and intensity of a peak in a pulse height spectrum is important for x-ray and $\gamma$-ray spectroscopy, charged-particle spectrometry, liquid chromatography, and many other subfields. However, both the "centroid" and "signal intensity" of a peak in a pulse-height spectrum are ill-defined quantities and different methods of analysis will yield different numerical results. Here, we apply three methods of analysis. Method A is based on simple count summation and is likely the technique most frequently applied in practice. The analysis is straightforward and fast, and does not involve any statistical modeling. We find that it provides reliable results only for high signal-to-noise data, but has severe limitations in all other cases. Method B employs a Bayesian model to extract signal counts and centroid from the measured total and background counts. The resulting values are derived from the respective posteriors and, therefore, have a rigorous statistical meaning. The method makes no assumptions about the peak shape. It yields reliable and relatively small centroid uncertainties. However, it provides relatively large signal count uncertainties. Method C makes a strong assumption regarding the peak shape by fitting a Gaussian function to the data. The fit is based again on a Bayesian model. Although Method C requires careful consideration of the Gaussian width (usually given by the detector resolution) used in the fitting, it provides reliable values and relatively small uncertainties both for the signal counts and the centroid. Show Chinese abstract

Abstract: 在脉冲高度谱中对峰的信号位置和强度进行估计对于X射线和$\gamma$-射线光谱学、带电粒子谱学、液相色谱法以及许多其他子领域都很重要。 然而，脉冲高度谱中峰的“质心”和“信号强度”都是定义不明确的量，不同的分析方法将产生不同的数值结果。 在这里，我们应用了三种分析方法。 方法A基于简单的计数求和，可能是实践中最常使用的技术。 该分析方法简单快速，不需要任何统计建模。 我们发现它仅在信噪比高的数据中能提供可靠的结果，而在其他所有情况下都有严重的局限性。 方法B采用贝叶斯模型从测得的总计数和背景计数中提取信号计数和质心。 所得值来自相应的后验分布，因此具有严格的统计意义。 该方法不对峰形做出任何假设。 它能提供可靠且相对较小的质心不确定性。 然而，它提供的信号计数不确定性相对较大。 方法C通过将高斯函数拟合到数据来对峰形做出强假设。 该拟合再次基于贝叶斯模型。 尽管方法C需要仔细考虑拟合中使用的高斯宽度（通常由探测器分辨率给出），但它能为信号计数和质心提供可靠且相对较小的不确定性。