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.

放射性碳年代测定值必须经过校准，鉴于大气中放射性碳水平的显著波动。然而，放射性碳年代域与日历年代域之间的映射并非一一对应，前提是校准曲线并非单射函数。传统的校准方法仅对放射性碳年代进行个别校准，而未考虑其时间/地层顺序。在多个方面，贝叶斯放射性碳年代建模方法相较于传统方法具有优势。首先，通过应用已知先验的一些约束条件，它能够提供比个别校准更为精确的年龄估计。其次，它可能为无法直接进行年代测定的考古特征或地质事件提供年龄估计。第三，它代表了一种灵活的统计推断方法。根据贝叶斯定理，先验信息可以以数学形式表述并整合到推断过程中，这可以通过马尔可夫链蒙特卡洛方法轻松实现。在此，提出了一种具有最小结构复杂度的层次贝叶斯模型。它为用户提供了一个灵活且强大的框架，将放射性碳年代序列化为一维连续体，从而最大限度地揭示其时间顺序，进而得出更为精确的时间点。附带的 Matlab 软件包不仅补充了现有的 MatCal 包，该包旨在对放射性碳年代进行个别校准，同时也作为在线放射性碳年代校准工具，如 OxCal 和 BCal 的替代品。