Internet Archaeol. 7. Buck et al.

Introduction

For many years archaeologists have used radiocarbon dating to help gain insight into the chronology of past human activity. Dateable organic material such as seeds or bone is now routinely submitted to radiocarbon dating laboratories for analysis. Such laboratories provide an estimate of the radiocarbon age of the material using analytical methods such as accelerator mass spectrometry. The radiocarbon determinations provided by such laboratories are, for various reasons, not on the calendar time scale. To be of greatest use in building archaeological chronologies, therefore, such determinations must be converted to the calendar scale via a suitable calibration curve. The process used to achieve this is known as calibration.

Several computer programmes exist to allow archaeologists to perform such calibrations and they are now broadly of two types. Those that allow the calibration of single determinations (such as CALIB) have been used for many years. Those that allow groups of related determinations to be calibrated all at the same time (such as BCal and OxCal) are a much more recent development and rely on Bayesian statistical methods developed by the present authors and colleagues over the last decade or so (see, for example, Buck et al. 1991; 1992; 1994a; 1994b; 1994c; Buck and Litton 1995; Christen 1994a; 1994b; Litton and Buck 1996; and Zeidler et al. 1998). The Bayesian radiocarbon calibration framework allows not only for the calibration of multiple determinations, but also for a priori relative and absolute chronological information (available from sources such as archaeological stratigraphy or dendrochronology) to be formally and coherently included in the interpretative process.

The Bayesian radiocarbon calibration framework

In formal terms the Bayesian radiocarbon calibration framework combines radiocarbon determinations with a priori chronological information and carefully constructed calibration curves, via appropriate statistical models, to arrive at posterior probability distributions for calendar dates of interest. The components of the framework can be summarised as follows.

Radiocarbon determinations

Each sample submitted to a radiocarbon dating laboratory for analysis gives rise to a radiocarbon determination. Such determinations are composed of two parts, an estimate of the radiocarbon age, and an error term which reflects the laboratory's uncertainty about the age estimate supplied. Both parts of the determination are required by BCal.

A priori chronological information

A priori chronological information commonly takes one of two forms: relative and absolute. Relative chronological information provides a priori insight into the order in which events took place. This type of information is commonly derived from stratigraphic evidence obtained during excavation. Absolute chronological information provides specific a priori temporal information about individual archaeological events of relevance to the current calibration. Examples of this type of information include date ranges within which certain events must have taken place, or estimates of specific calendar dates based on other absolute dating evidence (such as dendrochronology, coin evidence and the like).

Calibration curves

Calibration curves model the relationship between radiocarbon age and calendar years. Because radioactive carbon mixes differently in different environments, a different calibration curve is required when calibrating material from organisms that metabolised in different carbon reservoirs (for details see Stuiver and Braziunas 1993). A marine curve is normally used to calibrate the dates for material that metabolised in a marine environment (for example sea shell or fish bones), whereas an atmospheric curve should be used to calibrate the dates for material that metabolised in a terrestrial environment (such as wheat or barley seeds). BCal offers users access to both of the widely used internationally agreed calibration curves (Stuiver et al. 1998) and has a facility to allow utilisation of user-supplied curves too.

Appropriate statistical models

Collaborative work over the last decade or so (referred to in the Introduction) has given rise to statistical models that have been specifically formulated to allow coherent interpretation of radiocarbon determinations. These models are at the heart of the BCal software, but are not discussed here. Readers not familiar with them and who would like to know about the specific statistical models adopted might like to read chapter nine of Buck et al. (1996) in which they are described in detail.

Posterior probability distributions

The results of radiocarbon calibrations take the form of posterior probability distributions for the calendar dates of interest. Most archaeologists are now familiar with using and interpreting such distributions. BCal offers a flexible range of tools for viewing them to aid in the interpretation process.

Readers not fully familiar with radiocarbon calibration might like to read Bowman (1990) and some of the other material in the bibliography before progressing further with this paper. Those who are unfamiliar with Bayesian methods will find that Buck et al. (1996) provides an introduction aimed specifically at those interested in interpreting archaeological data.