A new conservative and robust Bayesian approach for the event date model in chronology building

Dating techniques in archaeology have undergone considerable development in recent decades. Today, the major challenge for archaeologists remains the reliability and precision of the date attributed to an artefact or an archaeological event. To this end, it is essential for archaeologists to cross-reference information from different sources (absolute dating, relative dating, typo-chronology, historical texts, etc.) The development of statistical models that are as close as possible to archaeological reasoning is necessary for efficient data processing. Research published over the past thirty years has shown that statistical models based on the Bayesian statistical approach are ideally suited to the construction of chronologies. Indeed, Bayesian modeling makes it possible to combine the chronometric measurements produced in dating laboratories and the expertise of archaeologists. Moreover, Bayesian statistics are also well suited to small samples (i.e., few dating data). In this article, we are interested in the event date model proposed by Lanos and Philippe in 2017. It is a hierarchical Bayesian model that allows combining chronometric dates assumed to be contemporaneous to estimate the date of a target event of historical interest. Irreducible errors between the chronometric dates and the event of interest are modeled with individual random effects, which makes it a model robust to outliers. However, the introduction of individual random effects can lead to imprecision of the posterior density of the event date. The aim of this article is to correct this imprecision by making the event date model conservative.

In this article, we first calculate the theoretical posterior densities of the parameters of the event date model proposed by Lanos and Philippe for two cases, namely the processing of chronometric measurements and the processing of typo-chronological observations. Secondly, we propose an improvement to this model by assuming randomness in the precision parameter, which we model here by a prior inverse-gamma distribution whose parameters are defined under the constraint of conservation of the event date distribution when it contains a single chronometric date. We illustrate this improvement by applying it to synthetic examples (usual distributions and calibrated distributions), then to data from various archaeological structures that have already been published.