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The data acts through a distribution called, third, the likelihood.
This refers to the unknown calendar date expressed when the radiocarbon age is converted into calendar years using the calibration curve, and the statistical uncertainty associated with it. A larger posterior probability occurs when the grouped calibrated dates agree with the data and are plausible in the light of the prior input into the model.
In the case of Area S, we had four stratum and four radiocarbon likelihoods from each, so an appropriate model for this archaeological sequence was constructed and is shown in Figure 6, alongside that from Area A. Bayesian analysis is mathematically intensive and analysis is only possible using computer programs, such as BCal,35 which incorporate simulation-based statistical tools called MCMC Markhov Chain Monte Carlo. For the user the archaeologistthese tools are now widely available and utilized in chronometric analysis.
What is interesting and crucially important is the use of suitably structured analysis models because when utilizing the Bayesian approach we are forced to make our model assumptions explicit through the prior.
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This has drawn attention to the fact that there are no true neutral assumptions that can be made in statistical analysis, Bayesian or otherwise, and that any model assumptions will have a real influence on the result. Once again, this is discussed in much greater details in some chapters in the book The Bible and 35 Buck et al.
By analyzing the posterior probabilities for these parameters, we are able to consider the modeled distribution of ages corresponding with termini post and ante quem, and also to test issues of contemporaniety and span. In addition to this, we can use our prior knowledge, not just of the archaeological sequence but also of the dated materials, to ascribe a probability as to whether or not a dated sample is likely to be an outlier in the model.
It could be, for example, that the variation in certain radiocarbon determinations might be due to sample constituent or contamination problems about which we had a prior hunch.
Outlier analysis is described by Christen37 in some detail. The low prior probability was given because of our knowledge of the screening of the charcoal samples and our sampling of external tree rings where possible. Nevertheless, the possibility of there being outliers was entertained. The resulting posterior probabilities were not significant and therefore we conclude there are no outliers in the dataset.
Note that the distribution is multi-modal, but that the highest probability as shown on the y axis is associated with c. We also analysed termini post and ante quem for KEN Table 4. These suggest, therefore, that the highest probability is that Area S was occupied after BC and Area A after BC in our paper, the former distribution was mistakenly stated as being before rather than after. A fuller methodological analysis would have made it obvious that this was not correct.
The discussion above is, we are afraid, rather moot in the light of more recent work, again in some chapters of The Bible and Radiocarbon Dating. Further dating of many more samples from KEN has produced a rather fuller picture of the chronology of the site. We now have a total of 19 determinations from Area S and 15 determinations from Area A. In general, these results corroborate the chronometric story described here and in the Antiquity paper, improve significantly the precision of our analysis and increase our confidence in the chronology of the site.
The reader is referred to this later work. The difference between the Cal BC date ranges in Table 1 of our Antiquity article, and the calendar age ranges discussed in the text itself, then, is due solely to the application of the Bayesian modeling. Table 1 simply represents radiocarbon calibrations, with no modelling. In the Antiquity text, the ranges represent posterior probabilities, computed in the light of the priors and the result of the modeled simulation of the data.
It is important to remember that our model assumptions can often make a significant influence on the resultant posterior distributions. We made this point earlier in our response to van der Steen and BienkowskiAntiquity by describing a hypothetical situation in which we treated two strata not as separate archaeological units, but as one. In an effort to test the sensitivity of our models, we also did the same thing in our more recent publication. It is important 39 Higham et al.
Further dating, or further excavation, or both, may cause us to revisit and modify our model. It is important to note, however, that this is a better approach than simply looking at the radiocarbon dates in isolation. They state that their attempts to replicate our results failed, but did not include the results of their analysis or consider why, when identical data was used, the results varied.
Again, it is likely that priors included within their model play a key role, and variation may be a result of this.
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This is not the case. The use of the former then, increases ones confidence in the age ranges obtained. The Bayesian analysis of Higham et al. Alternative scenarios are presented in Levy et al. Perhaps sometime down the line, all researchers interested in the Wadi Arabah will join together in a major research project that focuses on radiocarbon dating and the Iron Age of this important border zone.
Revue Biblique 73, pp. Excavations at Tawilan in Southern Jordan. Sheffield Archaeological Monographs 7. Evidence from Umm el-Biyara, Tawilan and Buseirah. A Reply to Finkelstein. The Archaeological Evidence from Transjordan. Edom and Seir in History and Tradition. Atlanta, Scholars Press, pp.
Busayra - Excavations by Crystal-M. British Academy Monographs in Archaeology No. Bayesian Approach to interpreting Archaeological Data. Chichester, John Wiley and Sons.
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The Holocene 13, pp. Applied Statistics 43, pp. Applied Statistics 47 4pp. Ancient Settlement of the Negev Highlands. Israel Antiquities Authority Report No. Jerusalem, Israel Antiquities Authority. Biblical Archaeologist 58, pp. A will provides orderly distribution of your property at death according to your wishes.
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