Skip to main content Accessibility help

Bayesian Analysis of Radiocarbon Dates

  • Christopher Bronk Ramsey (a1)


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.

    • Send article to Kindle

      To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Bayesian Analysis of Radiocarbon Dates
      Available formats

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Bayesian Analysis of Radiocarbon Dates
      Available formats

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Bayesian Analysis of Radiocarbon Dates
      Available formats



Hide All
Aguilar, DGP, Litton, CD, O'Hagan, A. 2002. Novel statistical model for a piece-wise linear radiocarbon calibration curve. Radiocarbon 44(1):195212.
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).
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):128.
Blaauw, M, Christen, JA. 2005. Radiocarbon peat chronologies and environmental change. Applied Statistics 54(4):805–16.
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.
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.
Boaretto, E, Jull, AJT, Gilboa, A, Sharon, I. 2005. Dating the Iron Age I/II transition in Israel: first intercomparison results. Radiocarbon 47(1):3955.
Bowman, SGE, Leese, MN. 1995. Radiocarbon calibration: current issues. American Journal of Archaeology 99(1):102–5.
Bronk Ramsey, C. 1994. Analysis of chronological information and radiocarbon calibration: the program OxCal. Archaeological Computing Newsletter 41:11–6.
Bronk Ramsey, C. 1995. Radiocarbon calibration and analysis of stratigraphy: the OxCal program. Radiocarbon 37(2):425–30.
Bronk Ramsey, C. 1998. Probability and dating. Radiocarbon 40(1):461–74.
Bronk Ramsey, C. 2000. Comment on ‘The use of Bayesian statistics for 14C dates of chronologically ordered samples: a critical analysis.’ Radiocarbon 42(2):199202.
Bronk Ramsey, C. 2001. Development of the radiocarbon calibration program. Radiocarbon 43(2A):355–63.
Bronk Ramsey, C. 2008. Deposition models for chronological records. Quaternary Science Reviews 27(1–2):4260.
Bronk Ramsey, C. 2009. Dealing with outliers and offsets in radiocarbon dating. Radiocarbon 51(3).
Bronk Ramsey, C, van der Plicht, J, Weninger, B. 2001. ‘Wiggle matching’ radiocarbon dates. Radiocarbon 43(2A):381–9.
Buck, CE, Millard, A. 2004. Tools for Constructing Chronologies: Crossing Disciplinary Boundaries. London: Springer. 257 p.
Buck, CE, Kenworthy, JB, Litton, CD, Smith, AFM. 1991. Combining archaeological and radiocarbon information: a Bayesian approach to calibration. Antiquity 65(249):808–21.
Buck, CE, Litton, CD, Smith, AFM. 1992. Calibration of radiocarbon results pertaining to related archaeological events. Journal of Archaeological Science 19(5):497512.
Buck, CE, Litton, CD, Scott, EM. 1994. Making the most of radiocarbon dating: some statistical considerations. Antiquity 68(259):252–63.
Buck, CE, Cavanagh, WG, Litton, CD. 1996. Bayesian Approach to Interpreting Archaeological Data. Chichester: Wiley. 402 p.
Buck, CE, Christen, JA, James, GN. 1999. BCal: an on-line Bayesian radiocarbon calibration tool. Internet Archaeology 7:
Christen, JA. 1994. Summarizing a set of radiocarbon determinations: a robust approach. Applied Statistics 43(3):489503.
Christen, JA. 2003. Bwigg: an internet facility for Bayesian radiocarbon wiggle-matching. Internet Archaeology 13:
Christen, JA, Litton, CD. 1995. A Bayesian approach to wiggle-matching. Journal of Archaeological Science 22(6):719–25.
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.
Cleal, R, Walker, KE, Montague, R. 1995. Stonehenge in Its Landscape: Twentieth-Century Excavations. London: English Heritage. 640 p.
Galimberti, M, Bronk Ramsey, C, Manning, SW. 2004. Wiggle-match dating of tree-ring sequences. Radiocarbon 46(2):917–24.
Gelfand, AE, Smith, AFM. 1990. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85(410):398409.
Gilks, WR, Richardson, S, Spiegelhalter, DJ. 1996. Markov Chain Monte Carlo in Practice. London: Chapman & Hall. 486 p.
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.
Jones, M, Nicholls, G. 1999. New radiocarbon calibration software. Radiocarbon 44(3):663–74.
Karlsberg, AJ. 2006. Flexible Bayesian methods for archaeological dating [unpublished PhD dissertation]. University of Sheffield.
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.
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.
Mazar, A, Bronk Ramsey, C. 2008. 14C dates and the Iron Age chronology of Israel: a response. Radiocarbon 50(2):159–80.
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 154:55107.
Nicholls, G, Jones, M. 2001. Radiocarbon dating with temporal order constraints. Applied Statistics 50(4):503–21.
Reimer, PJ, Brown, TA, Reimer, RW. 2004. Discussion: reporting and calibration of post-bomb 14C data. Radiocarbon 46(3):1299–304.
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.
Stuiver, M, Polach, HA. 1977. Discussion: reporting of 14C data. Radiocarbon 19(3):355–63.
Stuiver, M, Reimer, PJ. 1993. Extended 14C data base and revised CALIB 3.0 14C age calibration program. Radiocarbon 35(1):215–30.
Telford, RJ, Heegaard, E, Birks, HJB. 2004. The intercept is a poor estimate of a calibrated radiocarbon age. The Holocene 14(2):296–8.
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.
van der Plicht, J. 1993. The Groningen radiocarbon calibration program. Radiocarbon 35(1):231–7.
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):475520.
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.

Related content

Powered by UNSILO

Bayesian Analysis of Radiocarbon Dates

  • Christopher Bronk Ramsey (a1)


Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.