  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.
