Bayesian nonparametric estimation of the radiocarbon calibration curve

Abstract

The process of calibrating radiocarbon determinations onto the calendar scale involves, as a first stage, the estimation of the relationship between calendar and radiocarbon ages (the radiocarbon calibration curve) from a set of available high-precision calibration data. Traditionally the radiocarbon calibration curve has been constructed by forming a weighted average of the data, and then taking the curve as the piece-wise linear function joining the resulting calibration data points. Alternative proposals for creating a calibration curve from the averaged data involve a spline or cubic interpolation, or the use of Fourier transformation and other filtering techniques, in order to obtain a smooth calibration curve. Between the various approaches, there is no consensus as to how to make use of the data in order to solve the problems related to the calibration of radiocarbon determinations.

We propose a nonparametric Bayesian solution to the problem of the estimation of the radiocarbon calibration curve, based on a Gaussian process prior structure on the space of possible functions. Our approach is model-based, taking into account specific characteristics of the dating method, and provides a generic solution to the problem of estimating calibration curves for chronology building.

We apply our method to the 1998 international high-precision calibration dataset, and demonstrate that our model predictions are well calibrated and have smaller variances than other methods. These data have deficiencies and complications that will only be unravelled with the publication of new data, expected in early 2005, but this analysis suggests that the nonparametric Bayesian model will allow more precise calibration of radiocarbon ages for archaeological specimens.