End-to-end Bayesian analysis for summarizing sets of radiocarbon dates

Archaeologists and demographers increasingly employ aggregations of published radiocarbon (¹⁴C) dates as demographic proxies summarizing changes in human activity in past societies. Presently, summed probability densities (SPDs) of calibrated radiocarbon dates are the dominant method of using ¹⁴C dates to reconstruct demographic trends. Unfortunately, SPDs are incapable of converging on the distribution that generated a set of radiocarbon measurements, even when the number of observations is large. To overcome this problem, we propose a more principled alternative that combines finite mixture models and end-to-end Bayesian inference. Numerical simulations and an assessment of the statistical identifiability of our method demonstrate that it correctly converges on the generating distribution for two important models, exponentials and finite Gaussian mixtures, at least if the same statistical model is used to fit the data as was used to generate the data. To further validate this approach, we apply it to a set of radiocarbon dates from the Maya city of Tikal. We show that an end-to-end approach reconstructs with high accuracy expert demographic reconstructions based on settlement patterns and ceramics, but with more precise time-resolution and characterization of uncertainty than has heretofore been possible. Future work should consider alternatives to finite Gaussian mixtures for fitting the generating distribution.