Bayesian interpretation of radiocarbon results
Over the last thirty years radiocarbon dating has been widely used in archaeology and related fields to address a wide-range of chronological questions. Because of some inherent stochastic factors of a complex nature, radiocarbon dating presents a rich source of challenging statistical problems. The chronological questions posed commonly involve the interpretation of groups of radiocarbon determinations and often substantial amounts of a priori information are available. The statistical techniques used up to very recently could only deal with the analysis of one determination at a time, and no prior information could be included in the analysis. However, over the last few years some problems have been successfully tackled using the Bayesian paradigm. In this thesis we expand that work and develop a general statistical framework for the Bayesian interpretation of radiocarbon determinations. Firstly we consider the problem of radiocarbon calibration and develop a novel approach. Secondly we develop a statistical framework which permits the inclusion of prior archaeological knowledge and illustrate its use with a wide range of examples. We discuss various generic problems some of which are, replications, summarisation, floating chronologies and archaeological phase structures. The techniques used to obtain the posterior distributions of interest are numerical and, in most of the cases, we have used Markov chain Monte Carlo (MCMC) methods. We also discuss the sampling routines needed for the implementation of the MCNIC methods used in our examples. Thirdly we address the very important problem of outliers in radiocarbon dating and develop an original methodology for the identification of outliers in sets of radiocarbon determinations. We show how our framework can be extended to permit the identification of outliers. Finally we apply this extended framework to the analysis of a substantial archaeological dating problem.