Poisson Statistical Methods for the Analysis of Low-Count Gamma Spectra
Poisson Statistical Methods for the Analysis of Low-Count Gamma Spectra
复制标题
低计数伽马能谱分析的泊松统计方法
DOI：
10.1109/tns.2009.2020516
复制
发表时间：
2009
影响因子：
1.8
通讯作者：
B. Young
中科院分区：
文献类型：
--
作者：
John M. Kirkpatrick;B. Young
虽然放射性衰变是众所周知的是一个泊松过程，大多数的伽玛射线谱分析和计数技术，在今天常用的已经开发出的ldquoGaussian limitrdquo-也就是说，在明确的假设下，泊松分布可以很好地近似高斯分布。然而，当分布的平均计数为ldquosmallrdquo时，或者当尾部的行为（即，ldquomanyrdquo偏离平均值的标准偏差）是令人感兴趣的。我们看到越来越多的应用在不同的领域，从高能天体物理学和粒子物理学到安全检查和拦截，都属于这一范畴。在这些情况下，高斯方法的盲目应用可能会产生错误的，甚至是非物理的结果;特别是，依赖于检测决策的关键水平的高斯概念可能会对检测概率和误报率产生严重的不利影响。在本文中，已经开发了一套严格的泊松统计工具，使用一个简单的区域感兴趣（ROI）的方法，在低计数光谱的分析信号的检测和量化。这些工具在小峰的定量评估和定性检测方面都比传统的高斯方法提供了更高的准确性。公式推导出有意义的估计背景和信号（净峰面积）水平和它们的不确定性，并用于检测置信度的评价。虽然这些技术是在伽马能谱的背景下开发和提出的，但它们的适用性非常普遍，可以扩展到任何泊松统计预期适用的辐射或粒子探测场景，包括中子，α和β计数实验。
Although radioactive decay is well known to be a Poisson process, most of the gamma-ray spectral analysis and counting techniques in common use today have been developed in the ldquoGaussian limitrdquo-that is, under the explicit assumption that the Poisson distribution can be well approximated by the Gaussian distribution. However the Gaussian approximation is not valid when the mean number of counts of the distribution is ldquosmallrdquo, or when the behavior at the tails (i.e., ldquomanyrdquo standard deviations away from the mean) of the distribution is of interest. We see increasing numbers of applications in disparate fields, from high energy astrophysics and particle physics to security screening and interdiction that fall into this regime. The blind application of Gaussian methods in these cases can yield erroneous and even non-physical results; in particular, reliance on the Gaussian notion of Critical Levels for detection decisions can have serious detrimental effects on detection probabilities and false alarm rates. In this paper, a set of rigorous Poisson-statistical tools have been developed, using a straightforward region-of-interest (ROI) approach, for the detection and quantification of signals in the analysis of low-count spectra. These tools provide improved accuracy over traditional Gaussian methods in both the quantitative evaluation and qualitative detection of small peaks. Formulae are derived for meaningfully estimating background and signal (net peak area) levels and their uncertainties, and for the evaluation of detection confidence. While these techniques are developed and presented here in the context of gamma spectroscopy, their applicability is quite general and can be extended to any radiation or particle detection scenario where Poisson statistics are expected to apply, including neutron, alpha and beta counting experiments.