Non‐parametric calibration of multiple related radiocarbon determinations and their calendar age summarisation

Due to fluctuations in past radiocarbon (14$$ {}^{14} $$C) levels, calibration is required to convert 14$$ {}^{14} $$C determinations Xi$$ {X}_i $$ into calendar ages θi$$ {\theta}_i $$. 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(θ)$$ f\left(\theta \right) $$. Calibration of X1,…,Xn$$ {X}_1,\dots, {X}_n $$ can be improved significantly by incorporating the knowledge that the samples are related. Furthermore, summary estimates of the underlying shared f(θ)$$ f\left(\theta \right) $$ can provide valuable information on changes in population size/activity over time. Most current approaches require a parametric specification for f(θ)$$ f\left(\theta \right) $$ 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 multi‐modality typical within 14$$ {}^{14} $$C calibration. Our approach simultaneously calibrates the set of 14$$ {}^{14} $$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$$ {}^{14} $$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.