{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/non-parametric-calibration-of-multiple","title":"Non-parametric calibration of multiple related radiocarbon determinations and their calendar age summarisation","arxiv_id":"2109.15024","date":"2021-09-30","proceeding":null,"authors":["Timothy J Heaton"],"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.","url_abs":"https://arxiv.org/abs/2109.15024v2","url_pdf":"https://arxiv.org/pdf/2109.15024v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"non-parametric-calibration-of-multiple","repo_url":"https://github.com/tjheaton/nonparametriccalibration","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}