Using the Bayesian Method to Study the Precision of Dating by Wiggle-Matching

Abstract

The "wiggle-matching" technique has been widely used for the absolute dating of a series of radiocarbon-dated samples connected in one floating chronology. This is done by calculations of SS statistics (the mean-square distance of 14C ages of samples from the calibration curve) calculated for any assumed calendar age of the floating chronology. In the standard procedure the confidence intervals of true calendar age are derived from the width of the SS minimum, using the critical values of the chi-square distribution. This, however, seems oversimplified. Another approach is an extension of the Bayesian algorithm for calibration of single 14C dates. Here, we describe in detail the Bayesian procedure and discuss its advantages compared to the SS minimization method. Our calculations show that for given errors of 14C measurements, precision of dating the series is related to the shape of the SS curve around its minimum, rather than to the absolute value of SSmin. In some cases, dating precision may be improved more efficiently by extending the time span covered by the series rather than by improving the precision of the 14C measurements. The application of the Bayesian method enabled us to delimit the age of the floating varve chronology from the sediments of Lake Gościąż with distinctly better accuracy than was previously reported using the SS curve alone.