A New Robust Statistical Model for Radiocarbon Data

The general method currently used to analyze radiocarbon data ( y ) is conditional on the standard deviation (σ), reported by 14 C 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, σ is assumed as known in the statistical model for 14 C data used since the dawn of the discipline. This paper proposes a method for the analysis of 14 C data where the associated variance is taken as the product of an unknown constant α with the sum of the variance reported by the laboratory σ 2 and the variance of the calibration curve σ 2 (θ) (that is, an unknown error multiplier). Using this approach, assuming that the 14 C determination y arises from a Normal population and that, a priori, α has an inverse gamma distribution InvGa( a, b ), the resulting dating model is a t distribution with 2 a 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 14 C outlier analysis. Moreover, this new model might be a step forward in understanding and explaining the otherwise elusive scatter in 14 C data seen in interlaboratory studies.