A NEW ROBUST STATISTICAL MODEL FOR RADIOCARBON DATA

The general method currently used to analyze radiocarbon data (y) is conditional on the standard deviation (sigma), reported by C-14 laboratories, which reflects the uncertainty in the dating process. This uncertainty is measured through a series of empirical as well as theoretical considerations about the dating process, chemical preprocessing, etc. Nevertheless, sigma is assumed as known in the statistical model for C-14 data used since the dawn of the discipline. This paper proposes a method for the analysis of C-14 data where the associated variance is taken as the product of an unknown constant alpha with the sum of the variance reported by the laboratory sigma(2) and the variance of the calibration curve sigma(2)(theta) (that is, an unknown error multiplier). Using this approach, assuming that the C-14 determination y arises from a Normal population and that, a priori, alpha has an inverse gamma distribution InvGa(a, b), the resulting dating model is a t distribution with 2a degrees of freedom. The introduction of parameters a and b allows a robust analysis in the presence of atypical data and at the same time incorporates the uncertainty associated with the intra- and interlaboratory error assessment processes. Comparisons with the common Normal model show that the proposed t model produces smoother posterior distributions and seem to be far more robust to atypical data, presenting a simpler alternative to the standard C-14 outlier analysis. Moreover, this new model might be a step forward in understanding and explaining the otherwise elusive scatter in C-14 data seen in interlaboratory studies.