Characterisation of non-constant background in counting measurements

Abstract

A 'moving-target' method for characterising background in a counting measurement in which the instantaneous background count rate is a function of time, rather than being fixed, is proposed. This model treats the average Poisson mean in observation period P as coming from a gamma distribution with parameters αP and βP. This model is applied to a large dataset of replicate observations, consisting of 242 234U method blank measurements collected over a 2-y period. Point estimates of the model parameters are determined by comparing the mean and variance of the observed data and by maximising the likelihood function. Posterior distributions of the parameters are obtained by Markov Chain Monte Carlo. Assuming time-invariant fluctuations of the background count rate, the variation of the instantaneous count rate is described by a correlation function, which can be interpreted as describing how rapidly the background changes with time, or how likely the background is to change between measurements. An 'exponential- correlation' model of background time dependence is proposed, with parameters α, β and correlation time τ. Once determined, these parameters fully describe the distribution of background, just as NB and TB in the fixed-target model.