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.

由于大气放射性碳（radiocarbon）水平存在显著波动，因此必须对放射性碳年龄（radiocarbon age）进行校准。鉴于校准曲线并非单射函数（injective function），放射性碳年龄域到日历年龄（calendar age）域的映射并非一一对应。传统方法仅对放射性碳年龄进行单独校准，未考虑其时间或地层序列顺序。贝叶斯放射性碳年龄建模（Bayesian radiocarbon age modeling）在多个方面优于传统方法：其一，通过引入若干先验已知约束，其可提供比单独校准更为精准的年龄估算结果；其二，其可为无法直接定年的考古遗存或地质事件提供年龄估算结果；其三，其是一种灵活通用的统计推断方法。根据贝叶斯定理，可将先验信息以数学形式表述并整合至推断过程中，且可借助马尔可夫链蒙特卡洛（Markov chain Monte Carlo）方法轻松实现该流程。本文提出了一种结构复杂度最低的分层贝叶斯模型（hierarchical Bayesian model）。该模型可为用户提供一套灵活且强大的框架，能够将放射性碳年龄按照一维连续序列进行整合，以最优展现其时间序列顺序，进而获得更为精准的年代测定结果。随附的Matlab软件包不仅可补充现有专为单独校准放射性碳年龄设计的MatCal软件包，还可作为OxCal、BCal等放射性碳年龄校准在线工具的替代方案。

搜集汇总

背景与挑战

背景概述

该数据集是一个Matlab软件包，用于对放射性碳年龄进行贝叶斯校准，并考虑时间顺序约束，以提高年龄估计的精确性。它通过层次贝叶斯模型和马尔可夫链蒙特卡洛方法实现，可作为MatCal包的补充和OxCal等在线工具的替代方案。