A shot at a Bayesian model for data analysis in AMS measurements

A new Bayesian model for analysis of AMS-measurement data is presented. A first-order continuous autoregressive process is used to model the drift in the machine throughput or the modern reference level. Uncertainty for individual measurements is given by the 14C counting statistics. With the use of the autoregressive process the standard level for an unknown sample is estimated probabilistically and the parameters for this process are determined from the measurement data as a whole. Thus, the model is able to give reliable uncertainties even when the number of measurements is small. Simulations have been made to compare the novel method with the conventional mean-based method of data analysis. Problems related to the non-normality of the end result in the mean-based method are discussed. The present Bayesian model seems to give more accurate results and more rigorous error bounds.