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Bayesian Analysis of Radiocarbon Dates

Published online by Cambridge University Press:  18 July 2016

Christopher Bronk Ramsey
Christopher Bronk Ramsey*
Affiliation:
Research Laboratory for Archaeology, University of Oxford, Dyson Perrins Building, South Parks Road, Oxford, OX1 3QY. Email: christopher.ramsey@rlaha.ox.ac.uk
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Abstract

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If radiocarbon measurements are to be used at all for chronological purposes, we have to use statistical methods for calibration. The most widely used method of calibration can be seen as a simple application of Bayesian statistics, which uses both the information from the new measurement and information from the 14C calibration curve. In most dating applications, however, we have larger numbers of 14C measurements and we wish to relate those to events in the past. Bayesian statistics provides a coherent framework in which such analysis can be performed and is becoming a core element in many 14C dating projects. This article gives an overview of the main model components used in chronological analysis, their mathematical formulation, and examples of how such analyses can be performed using the latest version of the OxCal software (v4). Many such models can be put together, in a modular fashion, from simple elements, with defined constraints and groupings. In other cases, the commonly used “uniform phase” models might not be appropriate, and ramped, exponential, or normal distributions of events might be more useful. When considering analyses of these kinds, it is useful to be able run simulations on synthetic data. Methods for performing such tests are discussed here along with other methods of diagnosing possible problems with statistical models of this kind.

Type
Calibration
Information
Radiocarbon , Volume 51 , Issue 1 , 2009 , pp. 337 - 360
Copyright
Copyright © 2009 by the Arizona Board of Regents on behalf of the University of Arizona 

References

REFERENCES

Aguilar, DGP, Litton, CD, O'Hagan, A. 2002. Novel statistical model for a piece-wise linear radiocarbon calibration curve. Radiocarbon 44(1):195–212.CrossRefGoogle Scholar
Bayliss, A, Whittle, A, editors. 2007. Histories of the dead: building chronologies for five southern British long barrows [special issue]. Cambridge Archaeological Journal 17(Supplement S1).Google Scholar
Bayliss, A, Bronk Ramsey, C, van der Plicht, J, Whittle, A. 2007. Bradshaw and Bayes: towards a timetable for the Neolithic. Cambridge Archaeological Journal 17(Supplement S1):1–28.CrossRefGoogle Scholar
Blaauw, M, Christen, JA. 2005. Radiocarbon peat chronologies and environmental change. Applied Statistics 54(4):805–16.Google Scholar
Blaauw, M, Heuvelink, GBM, Mauquoy, D, van der Plicht, J, van Geel, B. 2003. A numerical approach to 14C wiggle-match dating of organic deposits: best fits and confidence intervals. Quaternary Science Reviews 22(14):1485–500.CrossRefGoogle Scholar
Blackwell, PG, Buck, CE. 2003. The Late Glacial human reoccupation of north-western Europe: new approaches to space-time modelling. Antiquity 77(296):232–40.CrossRefGoogle Scholar
Boaretto, E, Jull, AJT, Gilboa, A, Sharon, I. 2005. Dating the Iron Age I/II transition in Israel: first intercomparison results. Radiocarbon 47(1):39–55.CrossRefGoogle Scholar
Bowman, SGE, Leese, MN. 1995. Radiocarbon calibration: current issues. American Journal of Archaeology 99(1):102–5.Google Scholar
Bronk Ramsey, C. 1994. Analysis of chronological information and radiocarbon calibration: the program OxCal. Archaeological Computing Newsletter 41:11–6.Google Scholar
Bronk Ramsey, C. 1995. Radiocarbon calibration and analysis of stratigraphy: the OxCal program. Radiocarbon 37(2):425–30.CrossRefGoogle Scholar
Bronk Ramsey, C. 1998. Probability and dating. Radiocarbon 40(1):461–74.Google Scholar
Bronk Ramsey, C. 2000. Comment on ‘The use of Bayesian statistics for 14C dates of chronologically ordered samples: a critical analysis.’ Radiocarbon 42(2):199–202.CrossRefGoogle Scholar
Bronk Ramsey, C. 2001. Development of the radiocarbon calibration program. Radiocarbon 43(2A):355–63.CrossRefGoogle Scholar
Bronk Ramsey, C. 2008. Deposition models for chronological records. Quaternary Science Reviews 27(1–2):42–60.CrossRefGoogle Scholar
Bronk Ramsey, C. 2009. Dealing with outliers and offsets in radiocarbon dating. Radiocarbon 51(3).CrossRefGoogle Scholar
Bronk Ramsey, C, van der Plicht, J, Weninger, B. 2001. ‘Wiggle matching’ radiocarbon dates. Radiocarbon 43(2A):381–9.CrossRefGoogle Scholar
Buck, CE, Millard, A. 2004. Tools for Constructing Chronologies: Crossing Disciplinary Boundaries. London: Springer. 257 p.CrossRefGoogle Scholar
Buck, CE, Kenworthy, JB, Litton, CD, Smith, AFM. 1991. Combining archaeological and radiocarbon information: a Bayesian approach to calibration. Antiquity 65(249):808–21.CrossRefGoogle Scholar
Buck, CE, Litton, CD, Smith, AFM. 1992. Calibration of radiocarbon results pertaining to related archaeological events. Journal of Archaeological Science 19(5):497–512.CrossRefGoogle Scholar
Buck, CE, Litton, CD, Scott, EM. 1994. Making the most of radiocarbon dating: some statistical considerations. Antiquity 68(259):252–63.CrossRefGoogle Scholar
Buck, CE, Cavanagh, WG, Litton, CD. 1996. Bayesian Approach to Interpreting Archaeological Data. Chichester: Wiley. 402 p.Google Scholar
Buck, CE, Christen, JA, James, GN. 1999. BCal: an on-line Bayesian radiocarbon calibration tool. Internet Archaeology 7: http://intarch.ac.uk/journal/issue7/buck_index.html.Google Scholar
Christen, JA. 1994. Summarizing a set of radiocarbon determinations: a robust approach. Applied Statistics 43(3):489–503.CrossRefGoogle Scholar
Christen, JA. 2003. Bwigg: an internet facility for Bayesian radiocarbon wiggle-matching. Internet Archaeology 13: http://intarch.ac.uk/journal/issue13/christen_index.html.Google Scholar
Christen, JA, Litton, CD. 1995. A Bayesian approach to wiggle-matching. Journal of Archaeological Science 22(6):719–25.CrossRefGoogle Scholar
Christen, JA, Clymo, RS, Litton, CD. 1995. A Bayesian approach to the use of 14C dates in the estimation of the age of peat. Radiocarbon 37(2):431–41.CrossRefGoogle Scholar
Cleal, R, Walker, KE, Montague, R. 1995. Stonehenge in Its Landscape: Twentieth-Century Excavations. London: English Heritage. 640 p.Google Scholar
Galimberti, M, Bronk Ramsey, C, Manning, SW. 2004. Wiggle-match dating of tree-ring sequences. Radiocarbon 46(2):917–24.CrossRefGoogle Scholar
Gelfand, AE, Smith, AFM. 1990. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85(410):398–409.CrossRefGoogle Scholar
Gilks, WR, Richardson, S, Spiegelhalter, DJ. 1996. Markov Chain Monte Carlo in Practice. London: Chapman & Hall. 486 p.Google Scholar
Heegaard, E, Birks, HJB, Telford, RJ. 2005. Relationships between calibrated ages and depth in stratigraphical sequences: an estimation procedure by mixed-effect regression. The Holocene 15(4):612–8.CrossRefGoogle Scholar
Jones, M, Nicholls, G. 1999. New radiocarbon calibration software. Radiocarbon 44(3):663–74.Google Scholar
Karlsberg, AJ. 2006. Flexible Bayesian methods for archaeological dating [unpublished PhD dissertation]. University of Sheffield.Google Scholar
Kilian, MR, van der Plicht, J, van Geel, B. 1995. Dating raised bogs: new aspects of AMS 14C wiggle matching, a reservoir effect and climatic change. Quaternary Science Reviews 14(10):959–66.CrossRefGoogle Scholar
Manning, SW, Bronk Ramsey, C, Kutschera, W, Higham, T, Kromer, B, Steier, P, Wild, EM. 2006. Chronology for the Aegean Late Bronze Age 1700–1400 BC. Science 312(5773):565–9.CrossRefGoogle Scholar
Mazar, A, Bronk Ramsey, C. 2008. 14C dates and the Iron Age chronology of Israel: a response. Radiocarbon 50(2):159–80.CrossRefGoogle Scholar
Needham, S, Bronk Ramsey, C, Coombs, D, Cartwright, C, Pettitt, P. 1998. An independent chronology for British Bronze Age metalwork: the results of the Oxford Radiocarbon Accelerator Programme. Archaeological Journal 154:55–107.CrossRefGoogle Scholar
Nicholls, G, Jones, M. 2001. Radiocarbon dating with temporal order constraints. Applied Statistics 50(4):503–21.Google Scholar
Reimer, PJ, Brown, TA, Reimer, RW. 2004. Discussion: reporting and calibration of post-bomb 14C data. Radiocarbon 46(3):1299–304.Google Scholar
Steier, P, Rom, W. 2000. The use of Bayesian statistics for 14C dates of chronologically ordered samples: a critical analysis. Radiocarbon 42(2):183–98.CrossRefGoogle Scholar
Stuiver, M, Polach, HA. 1977. Discussion: reporting of 14C data. Radiocarbon 19(3):355–63.CrossRefGoogle Scholar
Stuiver, M, Reimer, PJ. 1993. Extended 14C data base and revised CALIB 3.0 14C age calibration program. Radiocarbon 35(1):215–30.CrossRefGoogle Scholar
Telford, RJ, Heegaard, E, Birks, HJB. 2004. The intercept is a poor estimate of a calibrated radiocarbon age. The Holocene 14(2):296–8.CrossRefGoogle Scholar
van den Bogaard, P. 1995. 40Ar/39Ar ages of sanidine phenocrysts from Laacher See Tephra (12,900 yr BP): chronostratigraphic and petrological significance. Earth and Planetary Science Letters 133(1–2):163–74.CrossRefGoogle Scholar
van der Plicht, J. 1993. The Groningen radiocarbon calibration program. Radiocarbon 35(1):231–7.CrossRefGoogle Scholar
Walker, MJC, Coope, GR, Sheldrick, C, Turney, CSM, Lowe, JJ, Blockley, SPE, Harkness, DD. 2003. Devensian lateglacial environmental changes in Britain: a multi-proxy environmental record from Llanilid, South Wales, UK. Quaternary Science Reviews 22(5–7):475–520.CrossRefGoogle Scholar
Zeidler, JA, Buck, CE, Litton, D. 1998. Integration of archaeological phase information and radiocarbon results from the Jama River Valley, Ecuador: a Bayesian approach. Latin American Antiquity 9(2):160–79.CrossRefGoogle Scholar