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Poisson vs. Gaussian statistics for sparse X-ray data: Application to the soft X-ray spectrometer

机译:泊松与高斯统计稀疏X射线数据的统计数据:应用于软X射线光谱仪

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摘要

Reliable results when fitting X-ray data require proper consideration of the statistics involved. We probe the impact of Gaussian versus Poisson statistics at low count levels using both the standard chi(2) method and maximum likelihood based on Poisson (C) statistics. The difference is studied and quantified through simulated spectra with known properties. We then test the results through analysis of Mn K alpha calibration data taken with the flight spare microcalorimeter for the Hitomi soft X-ray spectrometer. Through comparison with simulations, our results show that the chi(2) method tends to give overly optimistic estimates of the detector energy resolution, in particular when there are few counts. Given an energy resolution of similar to 5eV and a line with about 100 photons, the line width becomes similar to 10% lower in the chi(2) method than in Poisson statistics. This is a consequence of the uncertainties being dominated by counting statistics, and therefore highlights the need to choose the appropriate fit statistic.
机译:当拟合X射线数据时,可靠的结果需要适当考虑所涉及的统计数据。我们使用标准Chi(2)方法和基于Poisson(C)统计的最大可能性,探讨高斯与泊松统计的影响。通过具有已知性质的模拟光谱研究和定量差异。然后,我们通过分析用飞行备用微量微量微量仪进行HITMI软X射线光谱仪的Mn K alpha校准数据来测试结果。通过与模拟的比较,我们的结果表明,CHI(2)方法倾向于给出探测器能量分辨率的过度乐观估计,特别是当几乎没有计数时。考虑到类似于5EV的能量分辨率和大约100个光子的线,线宽在CHI(2)方法中比在泊松统计中变得相似。这是通过计数统计数据主导的不确定性的结果,因此强调需要选择适当的拟合统计数据。

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