A Bayesian approach to seriation problems in archaeology

In archaeology, the reconstruction of the relative chronology of objects (e.g. graves) is often based on absence/presence of information about finds (e.g. grave goods). Traditionally, this task is known as seriation. In this article the task is tackled by formulating a stochastic model for the relationship between the underlying grave order and the observed incidences and by analysing the data using the Bayesian method. In selecting a prior distribution the attempt has been to reflect the archaeological context, especially a potential preselection of specific types of finds suitable for the seriation task. In contrast to established methods for seriation, such as correspondence analysis, it is possible directly to describe the variability of the estimated order by analysing the posterior distribution of the order. Because the order of the graves is a non-numerical and high-dimensional parameter, special techniques for the analysis of the posterior distribution are required. Construction of a Markov chain Monte Carlo method to approximate the posterior distribution is also partially non-standard, since the distribution can be multi-modal and because a huge number of nuisance parameters are introduced to avoid parametric assumptions on the shape of the distribution of the types through time. An example illustrates the techniques and demonstrates the need for a sensitivity analysis in this setting. The framework of our approach can easily be extended either to adjust for known factors which influence the absence/presence or in order to incorporate prior information on the grave order.