Bayesian analysis of a radiation detection problem

Radioactive decay is a random process. As a result any measurement based on observing the radiation emitted during a nuclear decay is subject to statistical fluctuations. These fluctuations represent an unavoidable source of uncertainty in all nuclear measurements and often are the predominant source of imprecision or error [Knoll, 1989].Probability provides the best formalism for quantifying uncertainty. Probability distributions are used to express uncertainty[Morgan, 1990].In a nuclear counting experiment fluctuations are due to two major sources; the statistical nature of the radioactive decay process and the properties of the nuclear counting equipment (detector).Appropriate probability models were assigned to describe the uncertainty due to each source.The following is an outline of our analysis:a. Statistical modeling of the detection problem:1. The binomial distribution was selected to model the process of radioactive decay, where the initial sample contains N atoms and the number of atoms decaying is n.2. The binomial distribution was also selected to model the probability distribution for the number of atoms m a nuclear counter with efficiency &isin will detect from the n atoms that actually decayed.3. Uncertainty about &isin was described through analysis of the calibration procedure. Parts of this analysis, similar to the procedures of step one and two, were used to model the calibration of the standard source. We derived a statistical model for the absolute detector efficiency ∈.4. The uncertainty due to background was also considered and an expression for net count rate was derived.b. Results from the steps above were combined. The outcome is a probability distribution that estimates the activity and therefore the number of atoms in a sample from a given detector reading.