A new approach to radiocarbon summarisation: Rigorous identification of variations/changepoints in the occurrence rate of radiocarbon samples using a Poisson process

Abstract

A commonly-used paradigm to estimate changes in the frequency of past events or the size of populations is to consider the occurrence rate of archaeological/environmental samples found at a site over time. The reliability of such a “dates-as-data” approach is highly dependent upon how the occurrence rates are estimated from the underlying samples, particularly when calendar age information for the samples is obtained from radiocarbon (¹⁴C). The most frequently used “¹⁴C-dates-as-data” approach of creating Summed Probability Distributions (SPDs) is not statistically valid, or coherent, and can provide highly misleading inference. Here, we provide an alternative method with a rigorous statistical underpinning that also provides valuable additional information on potential changepoints in the rate of events. Furthermore, unlike current SPD alternatives, our summarisation approach does not restrict users to pre-specified, rigid, summary formats (e.g., exponential or logistic growth) but instead flexibly adapts to the dates themselves. Our methodology ensures more reliable “¹⁴C-dates-as-data” analyses, allowing us to better assess and identify potential signals present. We model the occurrence of events, each assumed to leave a radiocarbon sample in the archaeological/environmental record, as an inhomogeneous Poisson process. The varying rate of samples over time is then estimated within a fully-Bayesian framework using reversible-jump Markov Chain Monte Carlo (RJ-MCMC). Given a set of radiocarbon samples, we reconstruct how their occurrence rate varies over calendar time and identify if that rate contains statistically-significant changes, i.e., specific times at which the rate of events abruptly changes. We illustrate our method with both a simulation study and a practical example concerning late-Pleistocene megafaunal population changes in Alaska and Yukon.