Extra paper

BAYESIAN STATISTICS AND THE DATING OF ÇATALHÖYÜK EAST

Craig CESSFORD
Çatalhöyük research project, University College London, 31-34 Gordon Square,
London WC1H 0PY, UK.
cc250@cam.ac.uk

Introduction

By bringing together and presenting all the currently available radiocarbon dates for the Central Anatolian Neolithic, and other parts of Neolithic Anatolia, the CANeW team has simultaneously provided a highly useful resource and illustrated how meagre our data are. The number of sites that are dated is relatively small and many of these have only a small number of determinations. Even the sites with relatively large numbers of radiocarbon determinations are often not especially well endowed when one considers their size and number of phases of occupation. Given this situation, it is tempting to try and extrapolate as much as possible from the determinations that exist, but to be reliable such attempts must be as rigorous as possible. This is aided by a number of recent developments, which can be broadly considered to constitute the 'Third Generation' of radiocarbon dating (Taylor 1997:73), which means that radiocarbon dating is able to enter a new phase. These include accelerator mass spectrometry dating (ibid., 78-83) which allows more rigorous sample selection criteria, the availability of wiggle matched dendrochronological sequences (e.g. Newton and Kuniholm 1999), improved calibration (Stuiver et al. 1998) and the advent of powerful statistical modelling techniques (Bayliss 1998:101-104), particularly Bayesian statistics. It is now possible to introduce a greater amount of rigour and to begin to think of dating in terms of real calendar years and consider the actual duration of defined archaeological cultures, sites, phases within sites and comparisons between sites (see Evin 1995).

Bayesian statistics

The fundamental underlying principle of Bayesian statistics can be expressed as prior belief plus data equals posterior belief. They allow the incorporation of the archaeological understanding of a site into the statistical analysis of its dating and are of 'wide applicability to radiocarbon determinations from sites where good information exists about the relationship between the events being dated' (Buck et al. 1991:819; see also Buck et al. 1992, 1994a, 1994b, 1999, and http://bcal.sheffield.ac.uk/). The incorporation of such a priori knowledge can be viewed as corresponding well to the tenets of a post-processual interpretative archaeology. Thankfully it is only necessary to grasp underlying principles of the Bayesian statistical technique, not its complex minutiae, as good user-friendly packages for its implementation exist. A major handicap is that Bayesian statistics suffer from the GIGO principle of Garbage In Garbage Out. In particular if the model incorporates the idea that one determination is earlier than another, because this is stratigraphically correct, but this is not true for other reasons then the results will be misleading (Steier and Rom 2000). It always needs to be remembered that although around 95 % of radiocarbon determinations will fall within two standard deviations, even under perfect circumstances the remaining 5 %, or one in twenty, will fall outside this range. Circumstances are, however, far from perfect and especially when we are forced to rely on radiocarbon determinations from the 1960s and 1970s to date sites there are severe problems. Work in other areas has indicated that around one third of dates may have a discrepancy of two hundred years or more (Baillie 1990; Bruins and Van der Plicht 1998). The key concept with all dating is the relationship between the material being dated and the archaeological event that this is associated with. In many cases this relationship can be a tenuous one. Many Central Anatolian Neolithic dates are from charcoal, often from long-lived tree species such as oak and juniper, and may suffer from the 'old wood' problem, where the determination comes from heartwood that is centuries old when the tree is felled. Additionally it is likely that this wood, particularly large timbers, frequently had a considerable time-lag between felling and final deposition, perhaps being used for several purposes before being burnt and then being redeposited possibly more than once.

Both of these factors can produce a considerable time-lag effect and mean that the determination is likely to be older than the archaeological event that we are seeking to date. Many older determinations are also 'mixed' composites, where material from several separate items or contexts was combined to provide enough material for a single sample. Such composite samples are highly unreliable and ideally only single entities should be dated (Ashmore 1999). Many Neolithic sites in Central Anatolia are stratigraphically complex entities, particularly in the case of tell sites such as Çatalhöyük East. Residuality is an ever present danger in such circumstances, as has recently been demonstrated by the dating of both charred seeds and animal bones from the same contexts at Çatalhöyük East, where the results from the animal bones are sometimes several centuries older than those for the charred seeds (Unpublished determinations still undergoing final laboratory analysis at time of writing). Assessment of the reliability of determinations is frequently hindered by the failure to publish them properly. To be useful, publication of a determination must have its laboratory number, uncalibrated date, standard deviation, the precise nature and identification of the material dated, a consideration of the context that it is derived from and its stratigraphic relationship to any other determinations from the site.

The Çatalhöyük East sequence (For fuller discussions of the Çatalhöyük East sequence see Cessford 2001 and forthcoming)

At a practical level what tangible benefits has a Bayesian statistical analysis of the radiocarbon dating evidence from Çatalhöyük East produced? The first and most obvious benefit is that provided there is a reliable stratigraphical sequence, good sample selection and a reasonable number of determinations the temporal ranges of individual determinations can be markedly decreased. Often the improvement can be around twenty five to thirty five percent (Bayliss 1998:102), producing much more precise dates with the same degree of statistical likelihood. In fact in some instances the improvements can be much better than this (Table 1). Another major benefit is the identification of 'junk' or 'anomalous' determinations, that can be shown statistically not to fit within the overall sequence as they do not have a good relationship to the archaeological event from which they derive. Rather than intuitively selecting those determinations that fit with existing preconceptions and rejecting those that do not these assumptions can be tested. When applied to Çatalhöyük East this indicated that over half the radiocarbon determinations undertaken in the 1960s did not have a good relationship to the archaeological events they were supposed to be related to.

Table 1: Early dates from Çatalhöyük East showing their duration to 1 and 2 S.D. and the improvements from Bayesian analysis [NOTE FROM THE EDITORS - this table is superseding Table 1 in Craig Cessford's article in the CANeW book, where the cal BC ages at 1 S.D. normal and Bayesian were mixed]

Although it is often possible to date events of archaeological interest directly, some events by their very nature are undateable. The prime instance of this is the interface or transition between two archaeological phases or levels at a site. As these transitions are usually not represented by a specific physical deposit they often do not leave physical material suitable for dating purposes. They must therefore be dated on the basis of considering the determinations from both before and after the transition. In Bayesian analysis such interfaces are known as 'boundary parameters', which mark the beginning and end of a 'group', and they can be modelled and their probable date range calculated.

Rather than making rather intuitive generalisations about the relationships between various determinations, such as 'site X lasts for around Y hundred years' or 'sites X and Y are probably contemporary', much more rigorous statements can be made with precise statistical probabilities. At Çatalhöyük East the length of dated occupational sequence can now be calculated as between 890 to 1080 years (68 % probability) or 830 to 1220 years (95 % probability), whereas without Bayesian analysis it is likely that it would have been estimated as around a thousand years. Similarly at Asikli Höyük the dated deep sounding sequence can be shown to span 250 to 530 years (68 % probability) or 180 to 600 years (95 % probability). The overall dated sequence at Asikli Höyük is 420 to 760 years (68 % probability) or 250 to 870 years (95 % probability).

Such analysis also has an impact on important issues directly related to archaeological interpretation. The length of time individual buildings were likely to be occupied at Çatalhöyük East can be calculated as c. 50 to 80 years (68 % probability) or 45 to 90 years (95 % probability), greatly improving our ability to interpret these structures and their life histories. It is also possible to compare the sequences of different sites. When the Çatalhöyük East sequence is compared to the available radiocarbon determinations from Asikli Höyük then the probable interval between the latest determinations at Asikli Höyük can be compared to the earliest from Çatalhöyük East (Table 2). This, of course, only compares radiocarbon determinations. By utilising the information from Bayesian analysis combined with modelling of other factors, such as how much material is likely to have eroded from the top of Asikli Höyük and how likely it was that the very earliest occupation at Çatalhöyük East was encountered in the excavation area, we can state with a reasonable amount of confidence that the occupational sequences of Asikli Höyük and Çatalhöyük East are likely to have overlapped. Similarly we can compare the latest determination from Çatalhöyük East and as yet unpublished determinations from the base of the adjacent Chalcolithic site of Çatalhöyük West. The two determinations from Çatalhöyük West are between either 280 to 530 years (68 % probability) or 200 to 610 years (95 % probability) later than the determination from the Neolithic mound. This determination comes from Mellaart's level II, as levels I and 0 have not been dated. Allowance must be made for these two undated levels, plus even later levels that have probably been entirely eroded from the top of the mound, and the fact that material from Çatalhöyük West may not relate to the very earliest occupation. It is therefore probable that there was only a relatively brief interval between the occupation of the two sites, or possibly no interval at all. Such comparisons offer the possibility of greatly improving our ability to interpret the relationship between sites and their attendant material culture assemblages.

Table 2: Elapsed time between latest determinations at Asikli Höyük and earliest at Çatalhöyük East.

Conclusion

It is clear that Bayesian statistics have the potential to greatly improve our chronologies for the Central Anatolian Neolithic. In order to do this it is crucial that in future material for dating is carefully sampled, that reasonable numbers of determinations are undertaken and that they are selected as a coherent group so that they can be treated as a sequence as well as individually. Additionally it is crucial that these and already existing determinations are published in enough detail to allow full appraisal of the material dated and its context.

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