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

TL;DR

This paper introduces a non-parametric Bayesian method using Dirichlet process mixtures to calibrate related radiocarbon determinations, improving age estimates and revealing population activity patterns over time.

Contribution

It develops a novel non-parametric Bayesian calibration approach for related radiocarbon samples, avoiding parametric assumptions and enabling joint calibration and population activity analysis.

Findings

Improved age estimation through joint calibration of related samples.

Effective handling of multimodal calibration distributions.

Case studies demonstrating insights into population activity over time.

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.