  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.
