Bayesian Analysis of Radiocarbon Dates

TLDR

Radiocarbon dating requires statistical calibration, and Bayesian methods—using both new measurements and the calibration curve—provide a coherent framework for analyzing multiple dates and linking them to past events. This paper reviews the key model components, their mathematical formulation, and demonstrates their application in OxCal v4 for chronological analysis. The authors describe modular Bayesian models built from simple elements, discuss alternative distributional forms, and outline simulation and diagnostic methods for evaluating model performance.

Abstract

If radiocarbon measurements are to be used at all for chronological purposes, we have to use statistical methods for calibration. The most widely used method of calibration can be seen as a simple application of Bayesian statistics, which uses both the information from the new measurement and information from the 14 C calibration curve. In most dating applications, however, we have larger numbers of 14 C measurements and we wish to relate those to events in the past. Bayesian statistics provides a coherent framework in which such analysis can be performed and is becoming a core element in many 14 C dating projects. This article gives an overview of the main model components used in chronological analysis, their mathematical formulation, and examples of how such analyses can be performed using the latest version of the OxCal software (v4). Many such models can be put together, in a modular fashion, from simple elements, with defined constraints and groupings. In other cases, the commonly used “uniform phase” models might not be appropriate, and ramped, exponential, or normal distributions of events might be more useful. When considering analyses of these kinds, it is useful to be able run simulations on synthetic data. Methods for performing such tests are discussed here along with other methods of diagnosing possible problems with statistical models of this kind.