We developed a statistical theory of zero-count-detector (ZCD), which is defined as a zero-class Poisson under conditions outlined in the paper. ZCD is often encountered in the studies of rare events in physics, health physics, and many other fields where counting of events occurs. We found no acceptable solution to ZCD in classical statistics and affirmed the need for the Bayesian statistics. Several uniform and reference priors were studied and we derived Bayesian posteriors, point estimates, and upper limits. It was showed that the maximum-entropy prior, containing the most information, resulted in the smallest bias and the lowest risk, making it the most admissible and acceptable among the priors studied. We also investigated application of zero-inflated Poisson and Negative-binomial distributions to ZCD. It was showed using Bayesian marginalization that, under limited information, these distributions reduce to the Poisson distribution.

翻译：本文建立了零计数探测器（ZCD）的统计理论，该探测器被定义为在论文所述条件下的零类泊松分布。在物理学、健康物理学及许多其他涉及事件计数的领域进行罕见事件研究时，ZCD经常出现。经典统计学中未发现能解决ZCD问题的可接受方案，这证实了采用贝叶斯统计的必要性。本研究探讨了多种均匀先验与参考先验，推导了贝叶斯后验分布、点估计及上限。结果表明，包含最多信息的最大熵先验在研究所涉及的所有先验中偏差最小、风险最低，因此最具可采纳性与可接受性。此外，我们还研究了零膨胀泊松分布与负二项分布在ZCD中的应用。通过贝叶斯边际化方法证明，在信息有限的条件下，这些分布会退化为泊松分布。