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Non-parametric calibration of multiple related radiocarbon determinations and their calendar age summarisation
Applications · Submitted 30 Sep 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Due to fluctuations in past radiocarbon ($^{14}$C) levels, calibration is required to convert $^{14}$C determinations $X_i$ into calendar ages $\theta_i$. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s1 | 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 $f(\theta)$. | background 1.00 | 0.08 | 0.03 | asserted 0.83 |
| s2 | Calibration of $X_1, \ldots, X_n$ can be improved significantly by incorporating the knowledge that the samples are related. | background 0.95 | 0.14 | 0.22 | asserted 0.94 |
| s3 | Furthermore, summary estimates of the underlying shared $f(\theta)$ can provide valuable information on changes in population size/activity over time. | background 0.77 | 0.10 | 0.06 | asserted 0.61 |
| s4 | Most current approaches require a parametric specification for $f(\theta)$ which is often not appropriate. | gap 0.89 | 0.05 | 0.04 | asserted 0.94 |
| s5 | 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. | method 0.91 | 0.95 | 0.13 | asserted 1.00 |
| s6 | Our approach simultaneously calibrates the set of $^{14}$C determinations and provides a predictive estimate for the underlying calendar age of a future sample. | contribution 0.84 | 0.93 | 0.24 | asserted 1.00 |
| s7 | 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. | result 0.95 | 0.96 | 0.39 | asserted 1.00 |
| s8 | 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. | contribution 0.68 | 0.95 | 0.13 | asserted 0.99 |
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The paper
Original abstract
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.
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