A New Robust Statistical Model for Radiocarbon Data

Abstract

The general method currently used to analyze radiocarbon data (y) is conditional on the standard deviation (σ), reported by 14C 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 14C data used since the dawn of the discipline. This paper proposes a method for the analysis of 14C 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 σ2 and the variance of the calibration curve σ2(θ) (that is, an unknown error multiplier). Using this approach, assuming that the 14C 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 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 14C outlier analysis. Moreover, this new model might be a step forward in understanding and explaining the otherwise elusive scatter in 14C data seen in interlaboratory studies.