Bayesian inference for measurements of ionizing radiation under partial information

We derive a new Bayesian approach for estimating activity when partial information about the detection efficiency and the background activity is available. Explicit formulas based on the hypergeometric function are given for the mean and the variance of the obtained posterior distribution. A Monte Carlo method is developed that allows the results of the Bayesian procedure to be determined in a simple way. The proposed inference is illustrated by analyzing measurements of activity, and the results are compared with those obtained by applying a current ISO standard.