大型强子对撞机上基本粒子谱的经验贝叶斯展开
Empirical Bayes unfolding of elementary particle spectra at the Large Hadron Collider
摘要：
我们考虑所谓的展开问题，在实验高能物理，其中的目标是估计的真实光谱的基本粒子的观测扭曲的测量误差，由于有限的分辨率的粒子探测器。这是一个重要的统计逆问题，出现在欧洲核子研究中心的大型强子对撞机的数据分析。在数学上，该问题被形式化为一个间接观察到的泊松点过程的强度函数的估计。粒子物理学家特别热衷于展开方法，这些方法具有选择正则化强度的原则性方法，并允许量化解决方案中固有的不确定性。尽管实验物理学家已经考虑了许多方法，但可以说，这些方法中很少（如果有的话）以令人满意的方式处理这两个关键问题。在本文中，我们建议攻击的展开问题的框架内的经验贝叶斯估计：我们认为贝叶斯估计的系数的基础扩展的未知强度，使用正则化前，并采用蒙特卡罗期望最大化算法找到边际最大似然估计的超参数控制强度的正则化。由于超参数的数据驱动选择，使用经验贝叶斯后验得到的可信区间失去了它们的主观贝叶斯解释。由于这些间隔的性质和意义知之甚少，我们探索使用的bootstrap rescue构建纯粹的频率置信带的真实强度。所提出的方法的性能证明使用模拟和实际数据从大型强子对撞机。
英文摘要：
We consider the so-called unfolding problem in experimental high energy physics, where the goal is to estimate the true spectrum of elementary particles given observations distorted by measurement error due to the limited resolution of a particle detector. This an important statistical inverse problem arising in the analysis of data at the Large Hadron Collider at CERN. Mathematically, the problem is formalized as one of estimating the intensity function of an indirectly observed Poisson point process. Particle physicists are particularly keen on unfolding methods that feature a principled way of choosing the regularization strength and allow for the quantification of the uncertainty inherent in the solution. Though there are many approaches that have been considered by experimental physicists, it can be argued that few -- if any -- of these deal with these two key issues in a satisfactory manner. In this paper, we propose to attack the unfolding problem within the framework of empirical Bayes estimation: we consider Bayes estimators of the coefficients of a basis expansion of the unknown intensity, using a regularizing prior; and employ a Monte Carlo expectation-maximization algorithm to find the marginal maximum likelihood estimate of the hyperparameter controlling the strength of the regularization. Due to the data-driven choice of the hyperparameter, credible intervals derived using the empirical Bayes posterior lose their subjective Bayesian interpretation. Since the properties and meaning of such intervals are poorly understood, we explore instead the use of bootstrap resampling for constructing purely frequentist confidence bands for the true intensity. The performance of the proposed methodology is demonstrated using both simulations and real data from the Large Hadron Collider.
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