Probability theory provides a clear definition of what is meant by evidence in favor, against or none either way, of an event occurring for an unobserved response, via the principle of evidence. This is immediately applicable when carrying out a proper Bayesian analysis. Even without a prior, this imposes restrictions on reported inferences as these need to reflect the likelihood ordering. Relative belief inferences satisfy this requirement and, when the errors in these inferences are controlled, they also satisfy repeated sampling, or frequentist, requirements such as achieving given confidence levels. Relative belief inferences are considered here for the construction of intervals for uncertainty quantification in the context of a Poisson model for a signal with background noise. These intervals are contrasted with the well-known Feldman-Cousins intervals for this problem.

翻译：概率论通过证据原则，对未观测响应中事件发生的支持、反对或中性证据提供了明确定义。该原则在实施恰当的贝叶斯分析时直接适用。即便没有先验信息，这一原则也会对报告的推断施加约束，要求其必须反映似然排序。相对信念推断满足这一要求，并且当这些推断中的误差得到控制时，它们还满足重复抽样（即频率学派）要求，例如达到给定的置信水平。本文针对含背景噪声的信号泊松模型中的不确定性量化区间构建问题，探讨了相对信念推断方法。这些区间与著名的Feldman-Cousins区间在该问题中进行了对比分析。