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4. Bayesian Modelling

In this article we implement a Bayesian approach to modelling archaeological chronologies. This is an explicit, probabilistic method for estimating the dates when events happened in the past and for quantifying the uncertainties in these estimates. Lindley (1985) provides an accessible introduction to the principles of Bayesian statistics, Buck et al. (1996) introduce the approach from an archaeological viewpoint, and Bayliss et al. (2007a) more specifically provide an introduction to building Bayesian chronologies in archaeology.

All modelling has been undertaken using OxCal v4.2 (Bronk Ramsey 1995; 1998; 2009a; 2009b) and the calibration curve of Reimer et al. (2013). Weighted means of replicate measurements have been taken before incorporation in the model (Ward and Wilson 1978). The models are defined exactly by the brackets and OxCal CQL2 keywords on the left-hand side of Figures 2-7 and Figures 2, 4-7, and 9 (http://c14.arch.ox.ac.uk/). The posterior density estimates output by the model are shown in black, with the unconstrained calibrated radiocarbon dates shown in outline. The Highest Posterior Density intervals of the posterior density estimates produced by the models are given in italics, followed by a reference to the relevant parameter name and the figures in which the model which produced it is defined. Simple calibrated radiocarbon dates are given in normal type.

The currency of each lithic type is assumed to be a continuous, and relatively constant, period of activity (Buck et al. 1992). Only the earlier part of the chronological range of small scalene triangles, which were in use for a long period of time, is of relevance in comparison to Star Carr. For this reason, we have only included radiocarbon measurements associated with this type from sites that produced results before 8000 BP. Our modelled ending for the currency of small scalene triangles is thus arbitrary (but far enough from its beginning that the modelled estimate for the start of the type is probably robust).

A total of 305 radiocarbon measurements are included in our modelling, including the 200 measurements included in the chronological model for Star Carr reported by Milner et al. (in press, appendices 17.1 and 17.2) and 27 measurements included in the chronological model for Howick reported by Bayliss et al. (2007b, fig. 6.2 and table 6.1). Details of the other radiocarbon results included in the model are provided in Table 1. The overall form of the model is shown in Figure 2, with its individual components shown in Figures 3–7. It has good overall agreement (Amodel: 60).

Figure 2
Figure 2: Overall form of the chronological models for the currency of different microlith types in Britain

We have adopted various modelling approaches for each measurement dependent on the composition of the dated material and our understanding of the association between the dated sample and the relevant lithics. In a few cases, our perception of the accuracy of the reported measurement is also relevant. Our modelling approach for each measurement for Star Carr and Howick are described by Milner et al. (in press, chapter 17) and by Bayliss et al. (2007b) respectively, and those for the other radiocarbon dates included in the model are provided in Table 1. These are summarised by the following categories:

A total of 18 measurements fall in this latter category. As described in Milner et al. (in press, chapter 17), 13 of these are from Star Carr. Three are from Howick, two samples that are considered to be residual and one that is considered to be intrusive (Bayliss et al. 2007b, 71). A further sample relates to one of the bones from Flixton II, which was dated using the ion-exchange protocol at the Oxford Radiocarbon Accelerator Unit in 1996 (OxA-6329; Table 1; Hedges and Law 1989; Law and Hedges 1989). This measurement is 1000 BP later both than the other results on bones from Flixton II obtained by this method, and on the single result obtained on hydroxyproline (OxA-X-2395-14). It is also substantially later than the measurements on a waterlogged twig from the overlying peat (OxA-X-2495-12; Table 1). For these reasons, we regard OxA-6329 as anomalous. The considerable difficulties that have been encountered in obtaining reliable measurements on bone from this site should be noted (Marom et al. 2013). The last measurement that we consider inaccurate is Q-658 (10030±170 BP), a bulk sample of charred hazelnut shell from Thatcham III. This is almost 700 BP older than the recolonisation of hazel directly dated by AA-55306 (9314±55 BP) at the near adjacent palaeoenvironmental core from Thatcham reedbeds (Barnett 2009, 61–4).

We have constructed site-based model components for each site that has more than three radiocarbon dates. These sites are thus represented in the overall currency of the relevant lithics form by two parameters – the start and end of occupation at the site. This prevents our models being biased by the overwhelming number of measurements from just two sites. The model component relating to Star Carr is fully described and defined by Milner et al. (in press, appendices 17.1 and 17.2). Those for Howick, Cramond, and Kettlebury are fully defined respectively by Bayliss et al. (2007b, fig. 6.2) and Waddington et al. (2007, figs 15.12 and 15.17). Those for Flixton II, Seamer C, Seamer K, and Oakhanger are described below.

We have been able to gather details of more than 100 other radiocarbon measurements from archaeological contexts that fall within the time span of the lithic assemblages considered here (Table 2). These have been excluded from the modelling for a number of different reasons. In the majority of cases we have no reason to doubt the accuracy of the radiocarbon measurements themselves, but the dated samples lack a demonstrable link to a particular type of microlithic assemblage. Several determinations come from published sites that have few or no microliths, or a small range of types that are not particularly typologically distinctive. Some sites are not fully published, so details of the microlith forms that may be present are not currently available to us. A large group of sites are palimpsests, with a range of microlith forms of potentially differing dates. One such example is Thatcham Sewage works, where, though the majority of the assemblage is of Deepcar type, basally modified forms are also present. One radiocarbon date derives from this site, but there is currently no way to relate it to a specific lithic type. Another is Kinloch, Rhum, where, by contrast, the site is comparatively well dated, but has yielded huge quantities of lithic artefacts, including a wide range of microlith forms. The spread of radiocarbon dates indicates it was a focus of activities for a considerable period of time. For some such sites, further archive work may be able to demonstrate an association between a particular microlith type and a particular radiocarbon date. The reason why each sample has been excluded from the modelling is provided in Table 2.

We also note radiocarbon dates on a number of unassociated organic finds of Mesolithic date, such as the Wandsworth barbed points (Bonsall and Smith 1990) and on human bones, often from early cave excavations, where no contextual records remain (Meiklejohn et al. 2011). These cannot be associated with lithic forms and so are beyond the scope of this study.


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