Bayesian analysis for very-low-background counting of short-lived isotopes: Lowest minimum detectable quantity

Abstract

Conventional statistical analyses of counting measurements with a paired-count blank and sample yield unacceptably-large estimates of uncertainty that reduce measurement sensitivity when applied to very-low-background detection systems. An alternative is presented here: Bayesian analysis using longer-duration background measurements, appropriate modeling of the background, and a binomial distribution of decay-induced counts valid even for short-lived isotopes. We develop the needed formulae and demonstrate how the decision level and sample measurement duration are optimized jointly to produce the lowest minimum detectable quantity subject to constraints of specified acceptable risks of false detection and false failure to detect. A frequentist’s interpretation is maintained by using equal-likelihood prior distributions.