Flexible Bayesian methods for archaeological dating
Statistical models for the calibration of both independent and related groups of radiocarbon determinations are now well established and there exists a number of software packages such as BCal, OxCal and CALIB that can perform the necessary calculations to implement them. When devising new statistical models it is important to understand the motivations and needs of the archaeologists. When researchers select samples for radiocarbon dating, they are often not interested in when a specific plant or animal died. Instead, they want to use the radiocarbon evidence to help them to learn about the dates of other events, which cannot be dated directly but which are of greater historical or archaeological significance (e.g. the founding of a site). Our initial research focuses on formulating prior distributions that reliably represent a priori information relating to the rate of deposition of dateable material within an archaeological time period or phase. In archaeology, a phase is defined to be a collection of excavated material (context or layers) bounded early and late by events that are of archaeological importance. Current software for estimating boundary dates only allows for one possible type of a priori distribution, which assumes that material suitable for dating was deposited at a uniform rate between the start and end points of the phase. Although this model has been useful for many real problems, researchers have become increasingly aware of its limitations. We therefore propose a family of alternative prior models (with properties tailored to particular problems within archaeological research) which includes the uniform as a special case and allows for more realistic and robust modelling of the deposition process. We illustrate, via two case studies, the difference in archaeological conclusions drawn from the data when implementing both uniform and non-uniform prior deposition models. The second area of research, that we take the first steps towards tackling, is spatiotemporal modelling of archaeological calibration problems. This area of research is of particular interest to those studying the response of plants and animals, including humans, to climate change. In archaeological problems our temporal information typically arises from radiocarbon dating, which leads to estimated rather than exactly known calendar dates. Many of these problems have some form of spatial structure yet it is very rare that the spatial structure is formally accounted for. The combination of temporal uncertainty and spatial structure means that we cannot use standard models to tackle archaeological problems of this kind. Alongside this, our knowledge of past landscapes is generally very poor as they were often very different from modern ones; this limits the amount of spatial detail that can be included in the modelling. In this thesis we aim to make reliable inferences in spatio-temporal problems by carefully devising a model that takes account of the temporal uncertainty as well as incorporating spatial structure, to provide probabilistic solutions to the questions posed. We illustrate the properties of both the conventional models and the spatio-temporal models using a case study relating to the radiocarbon evidence for the Late glacial reoccupation of NW Europe.