Non-parametric calibration of multiple related radiocarbon determinations and their calendar age summarisation
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Due to fluctuations in past radiocarbon (^14C) levels, calibration is required to convert ^14C determinations X_i into calendar ages θ_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). Calibration of X_1, …, X_n can be improved significantly by incorporating the knowledge that the samples are related. Furthermore, summary estimates of the underlying shared f(θ) can provide valuable information on changes in population size/activity over time. Most current approaches require a parametric specification for f(θ) 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 ^14C calibration. Our approach simultaneously calibrates the set of ^14C 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 ^14C 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.
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