Chemical Caliborations

Bayesian Archaeology

Since archaeological problems are typified by being relatively data poor and prior information rich, there are strong philosophical arguments for routine use of the Bayesian paradigm in archaeological research. Indeed, a number of researchers argued for adoption of such methods long before Bayesian statistics were being routinely used in other disciplines. As a result, archaeology was one of the very first applied areas to benefit from the recent developments in Markov chain Monte Carlo (MCMC) simulation techniques. Now that we can implement tailor-made models for a wide range of problem types, Bayesian methods are really coming into their own.

Bayesian methods are an important aid to archaeological data interpretation because we very often have relatively little data but considerable, informative prior information which is complex and hard to interpret heuristically. The Bayesian framework provides us with a formal set of tools for incorporating subjective a priori information into the interpretive process and, as a result, it has proved useful to specialists in a number of sub-disciplines of archaeology including the following.

• Estimating the radiocarbon calibration curve. Due to sun-spot activity and to a range of other less well understood events, the amount of radioactive carbon in our atmosphere has not remained constant over time. Thus, in order to convert radiocarbon determinations obtained from a radiocarbon laboratory into true calender dates, we need a calibration curve derived from radiocarbon determinations for known age samples. Such calibration data exist and have been collated and updated for more than 25 years. All members of Sheffield's Bayesian archaeology research group have recently worked on this problem and Caitlin Buck was the statistician on the IntCal04 team that put together the internationally-agreed radiocarbon calibration curve (for more on this see below).
• Interpreting radiocarbon data from archaeological and environmental research projects. Once the radiocarbon calibration curve has been estimated, there is still a great deal of statistical work to do in utilising the curve to help date groups of related archaeological and/or environmental samples. Members of our research group have undertaken collaborative work in this area for many years (see below for publications). We continue to develop and improve the statistical tools available by devising tailored models in response to particular problems encountered by the user communities. Currently, we have two PhD students working on such problems. Angela Howard has English Heritage and EPSRC funding for a project with the title Robust and Flexible Tools for Archaeological Chronology Construction (supervised by Caitlin Buck and Paul Blackwell). Lynsey McColl is funded by NERC/EPSRC under their Environmental Mathematics and Statistics initiative and is jointly supervised by Caitlin Buck, Paul Pettitt (University of Sheffield Archaeology Department) and Andrew Millard (University of Durham Archaeology Department). Her project has the title Statistical Tools for Investigating Issues of Contemporaneity in Palaeo-environmental and Archaeological Records.
• Field survey. Field survey is now a vital part of archaeological research. It includes use of techniques like geophysical surveying (ground resistivity, magnetometry, ground penetrating radar and the like), collection and analysis of soil samples or cores (for soil phosphate, pollen, chemical composition analysis and the like) and field walking (in which teams of archaeologists walk across landscapes recording surface finds such as pottery, architectural stone and flint tools). Bayesian methods have been shown to be of particular interest in the interpretation of particularly noisy field survey results, in particular soil phosphate data. Since a great deal of organic material (both animal and vegetable) contains phosphate, human activity (particularly sedentary agricultural activity) often gives rise to higher levels of phosphate in the soil than those which arise naturally. Unfortunately, however, most of the rapid techniques available for soil phosphate surveying give rise to data which are noisy, contain missing values and are often on quite a coarse scale. Typically, all archaeologists are wishing to do with such data is to assign cells in the survey grid as either associated with previous human activity or not. Even this level of interpretation, however, proves difficult using heuristic methods. Bayesian change-point methods, which allow for the inclusion of prior information about the likely levels of phosphate (both `on-site' and `off-site') in any given landscape, have been shown to have considerable interpretive power.
• Structural analysis. Much of prehistoric architecture in Europe is simple and has well understood structural properties (such as dry stone walling or mud bricks). In Greece and several other parts of Europe, however, there exists a class of structures with structural properties that are far less will understood. These are known collectively as corbelled domes, but the specific examples in Sardinia are called nuraghi and in Greece they tend to be called tholoi. These structures are, in fact, not strictly `domes' since the more modern technique of vaulting is not used to enclose the space. Corbelling must be undertaken with great care if it is to be stable as it involves the enclosing of a roof space by over-sailing courses of masonry until the space is spanned. For some time, architectural historians and archaeologists have been fascinated by these structures and have sought to understand how prehistoric peoples would have constructed them and made them so stable. There are a number of ways in which Bayesian statisticians could help in the investigation of such issues and one that has proved quite successful is to use change point analysis to identify possible locations for changes in the form or profile of a particular structure. It is now clear that not all prehistoric corbelled domes were constructed in the same way. More work is still needed before we will understand whether corbelled domes in different places have similar or different structures and the nature of any spatial structure involved.
• Chemical compositional analysis. Chemical composition analysis is now used quite widely by archaeologists to help them understand about things like pottery manufacture, soil composition and alteration, and to aid in the identification of forgeries. Sometimes such data can be interpreted quite easily without the need for statistical methods - especially in the case of very poor forgeries for example. In situations where we wish to group objects or soil types together on the basis of chemical composition, however, we can be dealing with large arrays of data and complex questions relating to the similarities between samples or groups of samples. Since the data are often noisy, are prone to missing values, and we sometimes have quite informative prior information about the nature of the groupings we would expect, Bayesian cluster analysis has been applied to data of this type with some success.
• Building relative chronologies. One of the best established uses of formal mathematical methods in archaeology is as a tool to aid in construction of relative chronologies on the basis of artefact types found during excavation (in particular of human burials). The techniques used to do this have become known as seriation and rely on the assumption that artefact types come into use, stay in fashion for a while and finally go out of fashion without ever appearing again in the archaeological record. Early formal tools for helping with identifying likely chronological orderings on the basis of this assumption were either deterministic or used non-tailored statistical tools. More recently, however, a relatively simple Bayesian modelling of the problem has been implemented using MCMC, allowing any prior information about orderings and structure to be included in the seriation process.

These are just a few of the archaeology projects that members of the Bayesian cluster have been involved with over the years. For more about on-going research in this area see below and for more on other archaeological and environmental work in the Department see the pages for our Statistical Modelling and Applied Statistics cluster.