Papers › Non-parametric calibration of multiple related radiocarbon determinations and their...
Non-parametric calibration of multiple related radiocarbon determinations and their calendar age summarisation
Timothy J Heaton
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Due to fluctuations in past radiocarbon (¹⁴C) levels, calibration is required to convert ¹⁴C determinations Xᵢ into calendar ages θᵢ. 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 X₁, …, Xₙ 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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