背景源相关计数实验的客观贝叶斯分析
Objective Bayesian analysis of counting experiments with correlated sources of background
摘要：
在粒子物理、天体物理以及其他领域的计数实验中，经常会遇到微弱信号的探测问题。许多问题可以归结为信号与背景相互独立且服从泊松分布的模型。通常几个背景贡献同时存在，可能相关。我们提供了分析解决方案的统计推断问题，估计信号中存在的多个背景，在客观贝叶斯统计的框架。该模型可以写成单一泊松分布与多项分布的乘积的形式。前者与事件总数有关，后者描述了来自每个单独来源的事件的比例。不同背景之间的相关性可以通过适当地选择先验信息而包含在推理问题中。
英文摘要：
Searches for faint signals in counting experiments are often encountered in particle physics and astrophysics, as well as in other fields. Many problems can be reduced to the case of a model with independent and Poisson-distributed signal and background. Often several background contributions are present at the same time, possibly correlated. We provide the analytic solution of the statistical inference problem of estimating the signal in the presence of multiple backgrounds, in the framework of objective Bayes statistics. The model can be written in the form of a product of a single Poisson distribution with a multinomial distribution. The first is related to the total number of events, whereas the latter describes the fraction of events coming from each individual source. Correlations among different backgrounds can be included in the inference problem by a suitable choice of the priors.
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