An Information-Efficient Bayesian Model for AMS Data Analysis

Abstract

A Bayesian model for accelerator mass spectrometry (AMS) data analysis is presented. Instrumental drift is modeled with a continuous autoregressive (CAR) process, and measurement uncertainties are taken to be Gaussian. All samples have a parameter describing their true value. The model adapts itself to different instrumental parameters based on the data, and yields the most probable true values for the unknown samples. The model is able to use the information in the measurements more efficiently. First, all measurements tell something about the overall instrument performance and possible drift. The overall machine uncertainty can be used to obtain realistic uncertainties even when the number of measurements per sample is small. Second, even the measurements of the unknown samples can be used to estimate the variations in the standard level, provided that the samples have been measured more than once. Third, the uncertainty of the standard level is known to be smaller nearer a standard. Fourth, even though individual measurements follow a Gaussian distribution, the end result may not.For simulated data, the new Bayesian method gives more accurate results and more realistic uncertainties than the conventional mean-based (MB) method. In some cases, the latter gives unrealistically small uncertainties. This can be due to the non-Gaussian nature of the final result, which results from combining few samples from a Gaussian distribution without knowing the underlying variance and from the normalization with an uncertain standard level. In addition, in some cases the standard error of the mean does not represent well the true error due to correlations within the measurements resulting from, for example, a changing trend. While the conventional method fails in these cases, the CAR model gives representative uncertainties.