MatCalib: A Matlab software package for Bayesian calibration of radiocarbon ages subject to temporal order constraints

Radiocarbon ages must be calibrated due to the remarkable fluctuations of the atmospheric radiocarbon level. However, the map from the radiocarbon age domain to the calendar age domain is not one-on-one, providing that the calibration curve is not an injective function. The traditional method only calibrates the radiocarbon age individually, without considering their temporal/stratigraphical ordering. Bayesian radiocarbon age modeling is advantageous over the traditional method in several aspects. First, it can provide a more precise age estimate than the individual calibration by applying some constrains known a priori. Second, it may provide age estimates for an archaeological feature or a geological event that is unable to be dated directly. Third, it represents an adaptable method of statistical inference. According to Bayes’ theorem, the prior information can be formulated mathematically and integrated into the process of inference, which can be easily implemented using the Markov chain Monte Carlo method. Here, a hierarchical Bayesian model with a minimum level of structural complexity is presented. It provides users with a flexible and powerful framework to assemble radiocarbon ages into a sequence along a one-dimensional continuum so that it best reveals their temporal ordering, thereby yielding a more precise timing. The accompanying Matlab software package not only complements the existing MatCal package designed to calibrate radiocarbon ages individually, but also serves as an alternative to the online tools of radiocarbon age calibration such as OxCal and BCal.