Analysis of the abundance of radiocarbon samples as count data

The analysis of the abundance of radiocarbon samples through time has become a popular method to address questions of demography in archaeology. The history of this approach is marked by the use of the Sum of Probability Distributions (SPD), a key methodological development that first allowed researchers to visualize the abundance of radiocarbon samples on a calibrated temporal scale. However, the lack of a mathematical definition hinders the use of SPD in a proper statistical framework. Recent developments of model-based approaches have allowed a more rigorous statistical analysis of the abundance of radiocarbon data. Despite these advances, these methods inherit from the SPD an interpretation of the abundance of samples as a probability distribution. In this work we propose a change of perspective by treating radiocarbon data as count data. We present an approach that models the expected number of samples occurring at each year. We argue that this model provides more interpretable parameters and better accounts for the uncertainty in the number of samples. The performance of the proposed approach is evaluated through simulations and compared to an alternative state-of-the-art approach. Our new method is competitive with the state-of-the-art model. Furthermore, we demonstrate the computational burden of using the SPD as summary statistics under an approximate Bayesian computation analysis and propose more efficient summary statistics. Finally, we use a dataset of radiocarbon samples from Ireland and Britain to provide an application example. The results of these analyses are largely congruent with previous work on the same dataset except in revealing an earlier start of the Neolithic demographic expansion.