# The utility of a Bayesian analysis of complex models and the study of archeological ${}^{14}$C data

## TL;DR

This paper advocates for Bayesian analysis in complex ${}^{14}$C dating models, demonstrating its advantages and limitations through simulations and real data, and concludes that current data cannot resolve certain archaeological debates.

## Contribution

It introduces Bayesian methods for ${}^{14}$C dating models, highlighting their interpretability and practical use, while discussing their assumptions and limitations.

## Key findings

- Bayesian approach provides natural credible sets for complex models.
- Simulated toy models illustrate the impact of assumptions.
- Real data analysis shows current data cannot resolve Iron Age chronology debates.

## Abstract

The paper presents a critical introduction to the complex statistical models used in ${}^{14}$C dating. The emphasis is on the estimation of the transit time between a sequence of archeological layers. Although a frequentist estimation of the parameters is relatively simple, confidence intervals constructions are not standard as the models are not regular. I argue that that the Bayesian paradigm is a natural approach to these models. It is simple, and gives immediate solutions to credible sets, with natural interpretation and simple construction. Indeed it is the standard tool of ${}^{14}$C analysis. However and necessarily, the Bayesian approach is based on technical assumptions that may dominate the scientific conclusion in a hard to predict way. I exemplify the discussion in two ways. Firstly, I simulate toy models. Secondly, I analyze a particular data set from the Iron Age period in Tel Rehov. These data are important to the debate on the absolute time of the Iron Age I/IIA transition in the Levant, and in particular to the feasibility of the Bible story about the United Monarchy of David and Solomon. Our conclusion is that the data in question cannot resolve this debate.