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

https://doi.org/10.1016/j.jas.2021.105473Get rights and content
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Highlights

  • Summed probability densities (SPDs) cannot reconstruct the generating distribution.

  • We present a statistical method that can recover the generating distribution.

  • Our method is end-to-end, Bayesian, and uses mixtures of Gaussians.

  • When applied to data from the site of Tikal, our reconstruction accords well with previous expert population estimates.

Abstract

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.

Keywords

Radiocarbon
Bayesian statistics
Equifinality
Tikal
Maya
Demography
Summed probabilities

Data Availability and Code Availability

The MesoRAD database is archived with tDAR (The Digital Archaeological Record) with the doi 10.6067/XCV8458587. The data are also available in the file MesoRAD-v.1.2_no_locations.xlsx in the GitHub repository at: https://github.com/MichaelHoltonPrice/price_et_al_tikal_rc. Latitude/longitude locations have been removed from the publicly available data. The R package baydem is available on GitHub at: https://github.com/eehh-stanford/baydem. The precise results used for this paper are permanently archived on Zenodo with the doi 10.5281/zenodo.5294902

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