Improved parameter estimation and uncertainty propagation in Bayesian Radiocarbon-dated Event Count [REC] models

Data about the past contain chronological uncertainty that needs to be accounted for in statistical models. Recently a method called Radiocarbon-dated Event Count (REC) modelling has been explored as a way to improve the handling of chronological uncertainty in the context of statistical regression. REC modelling has so far employed a Bayesian hierarchical framework for parameter estimation to account for chronological uncertainty in count series of radiocarbon-dates. This approach, however, suffers from a couple of limitations. It is computationally inefficient, which limits the amount of chronological uncertainty that can be accounted for, and the hierarchical framework can produce biased, but highly precise parameter estimates. Here we report the results of an investigation in which we compared hierarchical REC models to an alternative with simulated data and a new R package called "chronup". Our results indicate that the hierarchical framework can produce correct high-precision estimates given enough data, but it is susceptible to sampling bias and has an inflated Type I error rate. In contrast, the alternative better handles small samples and fully propagates uncertainty into parameter estimates. In light of these results, we think the alternative method is more generally suitable for Palaeo Science applications.