Bayesian Approach to Interpreting Archaeological Data.

Batt, Cathy

A volume on Bayesian statistics may not be top of every archaeologist's reading list, but the techniques discussed in this book are likely to have increasing influence on the quantification and interpretation of archaeological data. The Bayesian approach to statistical analysis of data and their subsequent interpretation differs from conventional statistical methods principally in that it allows relevant prior knowledge or beliefs to be formally incorporated into analyses. Thus, a logical framework is established in which beliefs are updated from those held before observing the data, to those held after taking the data into account. What this approach offers to archaeological problem-solving is a mathematically and statistically rigorous framework within which to bring together data from a variety of sources and specialisms into a single analysis, for example the combination of radiocarbon determinations with stratigraphic information to refine the interpretation of both. As Buck et al. acknowledge, Bayesian methods have their critics, both inside and outside archaeology, particularly because they introduce an element of personal judgement into the statistical model. In many ways, however, the Bayesian approach, with its emphasis on explicit treatment of prior beliefs about an archaeological question and the modelling of possible outcomes, merely formalizes mathematically what is already accepted as good archaeological practice.

Whilst conceptually elegant and intuitively attractive, it has taken over 200 years for the Rev. Thomas Bayes' concepts of 'inverse probability' to find wide acceptance and their use in archaeology is still in its infancy. The main restrictions have been conceptual difficulties in expressing prior beliefs in a mathematical manner and in the number of calculations required, partially solved by modern computing power. The authors suggest that this timing is fortuitous for archaeological applications, as it coincides with an increasingly questioning approach to archaeological data and an awareness of the underlying assumptions made in interpreting them.

In this book Buck et al. have brought together their work on Bayesian approaches to archaeological questions with the intention of introducing the method and its applications primarily to students of archaeology and professional archaeologists, although the topic is also clearly of interest to those in related disciplines. The book comprises an informal introduction (chapters 1 and 2), the underlying principles of Bayesian approach and practice (chapters 3 to 8) and a series of case-studies (chapters 9 to 12). The authors assume little prior mathematical and statistical knowledge, and the initial chapters provide an excellent introduction to areas such as mathematical and statistical modelling in archaeology and probability theory, leading into a more focused discussion of Bayesian inference and implementation.

Despite the potentially daunting subject matter, Buck et al. have produced a commendably readable volume. Written in a clear, explanatory style, it leads the reader through the subject, from considerations of designing a toy elephant and mathematical models for getting to the airport on time, to Markov chain Monte Carlo methods and use of the Gibbs sampler. Inevitably, a journey from basic statistical approaches right up to the cutting edge of research is a somewhat rapid and unsettling experience, and may leave the less statistically minded reader with a feeling akin to jet-lag by the end. However, it is certainly a journey worth making for the views and insights on the way. Conversely, unless the reader is familiar with the terminology established in the early chapters, it is difficult to dip into the book, for example simply to look at the results of the case-studies. Key to the accessibility of the text is the use of simple illustrative examples throughout. Whenever a new argument is introduced, there is always an example on the next page to clarify it. The intention to make the book appropriate for archaeologists, and the balance of archaeological and statistical expertise of the authors, is borne out in the wide variety of archaeological examples, which include corbelling in Minoan tombs, otolith size as an indicator of seasonality in fishing, disease patterns in past populations and size of clay-pipe moulds. The initial examples are necessarily simplistic, but the later case-studies involve the application of Bayesian methods to genuine and complex archaeological questions.

The case-studies involving radiocarbon dating are the most highly developed and outline the area in which these methods are currently having most impact, as evidenced by their inclusion in the widely available radiocarbon calibration and stratigraphic analysis program, Oxcal (Ramsey 1994). The examples chosen deal with archaeological issues familiar to regular users of radiocarbon dating, including use of stratigraphic information alongside radiocarbon determinations to give reduced calendar-date ranges, determining the time interval between events dated by radiocarbon and dealing with groups of radiocarbon determinations which include rogue measurements. It is certainly in the field of radiocarbon dating that Bayesian methods have best demonstrated their potential and these sections are recommended reading for all those wishing systematically to integrate radiocarbon determinations with other site data. However, the case-studies also point the way towards other applications, such as the spatial analysis of site survey and prospection data, the contentious issues of sourcing and provenancing, as well as applications to other dating methods. All these areas clearly need more statistical investigation before widespread acceptance, but the potential of the Bayesian approach cannot be ignored.

This book emphasizes throughout, and is itself an example of, the value of collaboration between archaeologists and statisticians. It certainly does not offer do-it-yourself recipes for applying Bayesian statistics (these might be somewhat indigestible!), as the nature of the approach is that each problem has to be tackled afresh with a new model and expression of prior beliefs. However, if Bayesian approaches continue their rapid development along the lines indicated by Buck et al., then this volume is well-placed to become the standard text and recommended reading for an increasing number of archaeologists.

CATHY BATT Department of Archaeological Sciences University of Bradford

Reference

RAMSEY, C.B. 1994. Analysis of chronological information and radiocarbon calibration: the program, Archaeological Computing Newsletter 41: 11-16.