Uncertain beginnings: a comparison of the accuracy and precision of methods estimating extreme chronological events

Finding the earliest and latest occurrences of phenomena has always been one of the main concerns of archaeology, palaeontology and conservation biology. For all these disciplines, the first or last occurrences of the phenomenon under investigation will almost always be absent from known records. This known absence forces researchers to develop inferential tools that examine available samples to estimate the dates of the earliest and latest occurrences. Several methods have been developed, used, and tested in previous studies. Here, we compare three methods against simulated datasets to systematically assess their performance in estimating ‘origination events’ in terms of accuracy (whether interval estimates include the true and unobserved earliest date) and precision (the width of the interval estimates). We consider different variants of Optimal Linear Estimation (OLE), Bayesian Phase Modelling (BPM), and Calibration-Resampled Inverse-Weighted McInerny Method (CRIWM). All three classes of methods have been applied within archaeological or biological contexts, or both, but a formal comparative assessment of their strengths and weaknesses is currently lacking. We perform this analysis using an extensive tactical simulation, allowing us to assess the strengths and weaknesses of each approach.