标题： 关于开关问题：一种客观贝叶斯分析 显示英文标题

标题： On the On-Off Problem: An Objective Bayesian Analysis

摘要： 关-开问题，也称为李-马问题，是一个统计问题，其中测量的速率是两部分的总和。 第一部分是由信号引起的，第二部分是由背景引起的，这两部分都是未知的。 大多数使用的是频率学派的解决方案，这些方法仅适用于计数较多的情况。 当事件稀少时，这种近似就不够好了。 实际上，在高能天体物理学中，这种情况通常是常态而非例外。 我将提出一种通用的客观贝叶斯解决方案，该方案仅依赖于关-开问题的前三个参数： “关”区域中的事件数、“开”区域中的事件数以及它们的暴露比例。 通过两步方法，可以以统一的方式推断信号的显著性、强度、不确定度或上限。 该方法在没有任何限制的情况下适用于任何计数，包括零，并且可以在粒子物理、宇宙射线物理和高能天体物理学中广泛应用。 我将该方法应用于伽马射线暴数据。 显示英文摘要

摘要： The On-Off problem, aka. Li-Ma problem, is a statistical problem where a measured rate is the sum of two parts. The first is due to a signal and the second due to a background, both of which are unknown. Mostly frequentist solutions are being used that are only adequate for high count numbers. When the events are rare such an approximation is not good enough. Indeed, in high-energy astrophysics this is often the rule rather than the exception. I will present a universal objective Bayesian solution that depends only on the initial three parameters of the On-Off problem: the number of events in the "on" region, the number of events in the "off" region, and their ratio-of-exposure. With a two-step approach it is possible to infer the signal's significance, strength, uncertainty or upper limit in a unified a way. The approach is valid without restrictions for any count number including zero and may be widely applied in particle physics, cosmic-ray physics and high-energy astrophysics. I apply the method to Gamma Ray Burst data.