Due to fluctuations in past radiocarbon ($^{14}$C) levels, calibration is required to convert $^{14}$C determinations $X_i$ into calendar ages $\theta_i$. In many studies, we wish to calibrate a set of related samples taken from the same site or context, which have calendar ages drawn from the same shared, but unknown, density $f(\theta)$. Calibration of $X_1, \ldots, X_n$ can be improved significantly by incorporating the knowledge that the samples are related. Furthermore, summary estimates of the underlying shared $f(\theta)$ can provide valuable information on changes in population size/activity over time. Most current approaches require a parametric specification for $f(\theta)$ which is often not appropriate. We develop a rigorous non-parametric Bayesian approach using a Dirichlet process mixture model, with slice sampling to address the multimodality typical within $^{14}$C calibration. Our approach simultaneously calibrates the set of $^{14}$C determinations and provides a predictive estimate for the underlying calendar age of a future sample. We show, in a simulation study, the improvement in calendar age estimation when jointly calibrating related samples using our approach, compared with calibration of each $^{14}$C determination independently. We also illustrate the use of the predictive calendar age estimate to provide insight on activity levels over time using three real-life case studies.
翻译:由于过去的放射性碳(++14美元)水平的波动,需要校准将美元14美元(X_I)美元(美元)的确定值转换成日历年龄($theta_i美元)。在许多研究中,我们希望校准从同一地点或背景中采集的一组相关样本,这些样本的日历年数来自相同共享但未知的密度(美元)美元(美元)。通过纳入样本相关知识,可以大大改进X_1美元(美元)的校准。此外,对基底共享美元(美元)的估算值可以提供关于人口规模/活动随时间变化的宝贵信息。大多数当前方法都需要对美元(美元)或上下文中的一组相关样本进行参数性说明,而这些样本通常不合适。我们利用Drichlet进程混合模型制定严格的非参数性巴耶斯办法,通过切片取样解决典型的多式(美元14美元)C校准成本。我们的方法同时校准美元(美元)的确定值(美元)C)的一套确定值,并提供美元预测性估算值(美元)时间(美元)的精确度估计数,用于对未来校准样本的每个校准年龄进行对比研究时,我们用相关的校准的校准的校准的校准的校准的校准分析。