Skip to main content

Methods for Summarizing Radiocarbon Datasets

  • Christopher Bronk Ramsey (a1)

Bayesian models have proved very powerful in analyzing large datasets of radiocarbon (14C) measurements from specific sites and in regional cultural or political models. These models require the prior for the underlying processes that are being described to be defined, including the distribution of underlying events. Chronological information is also incorporated into Bayesian models used in DNA research, with the use of Skyline plots to show demographic trends. Despite these advances, there remain difficulties in assessing whether data conform to the assumed underlying models, and in dealing with the type of artifacts seen in Sum plots. In addition, existing methods are not applicable for situations where it is not possible to quantify the underlying process, or where sample selection is thought to have filtered the data in a way that masks the original event distribution. In this paper three different approaches are compared: “Sum” distributions, postulated undated events, and kernel density approaches. Their implementation in the OxCal program is described and their suitability for visualizing the results from chronological and geographic analyses considered for cases with and without useful prior information. The conclusion is that kernel density analysis is a powerful method that could be much more widely applied in a wide range of dating applications.

Corresponding author
*Corresponding author. Email:
Hide All

Selected Papers from the 8th Radiocarbon & Archaeology Symposium, Edinburgh, UK, 27 June–1 July 2016

Hide All
Andersen KK, Azuma N, Barnola J-M, Bigler M., Biscaye P, Caillon N, Chappellaz J, Clausen HB, Dahl-Jensen D, Fischer H, et al. 2004. High-resolution record of Northern Hemisphere climate extending into the last interglacial period. Nature 431(7005):147151.
Armit I, Swindles GT, Becker K. 2013. From dates to demography in later prehistoric Ireland? Experimental approaches to the meta-analysis of large 14C data-sets. Journal of Archaeological Science 40(1):433438.
Armit I, Swindles GT, Becker K, Plunkett G, Blaauw M. 2014. Rapid climate change did not cause population collapse at the end of the European Bronze Age. Proceedings of the National Academy of Sciences 111(48):1704517049.
Bamforth DB, Grund B. 2012. Radiocarbon calibration curves, summed probability distributions, and early Paleoindian population trends in North America. Journal of Archaeological Science 39(6):17681774.
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(S1):128.
Bigler M. 2004. Hochaufl ̈osende Spurenstoffmessungen an polaren Eisbohrkernen: Glaziochemis- che und klimatische Prozessstudien [unpublished PhD dissertation]. University of Bern, Switzerland.
Botev ZI, Grotowski JF, Kroese DP. 2010. Kernel density estimation via diffusion. Annals of Statistics 38(5):29162957.
Bronk Ramsey C. 2009. Bayesian analysis of radiocarbon dates. Radiocarbon 51(1):337360.
Bronk Ramsey C, Lee S. 2013. Recent and Planned Developments of the Program OxCal. Radiocarbon 55(2-3):720730.
Buchanan B, Collard M, Edinborough K. 2008. Paleoindian demography and the extraterrestrial impact hypothesis. Proceedings of the National Academy of Sciences 105(33):1165111654.
Buck CE, Litton CD, Smith AFM. 1992. Calibration of radiocarbon results pertaining to related archaeological events. Journal of Archaeological Science 19(5):497512.
Contreras DA, Meadows J. 2014. Summed radiocarbon calibrations as a population proxy: a critical evaluation using a realistic simulation approach. Journal of Archaeological Science 52:591608.
Culleton BJ. 2008. Crude demographic proxy reveals nothing about Paleoindian population. Proceedings of the National Academy of Sciences. E111.
Gilks WR, Richardson S, Spiegelhalter DJ. 1996. Markov Chain Monte Carlo in Practice. London:Chapman & Hall.
Ho SYW, Shapiro B. 2011. Skyline-plot methods for estimating demographic history from nucleotide sequences. Molecular Ecology Resources 11(3):423434.
Karlsberg AJ. 2006. Statistical modeling for robust and flexible chronology building [PhD thesis]. University of Sheffield.
Kerr T, McCormick F. 2014. Statistics, sunspots and settlement: influences on sum of probability curves. Journal of Archaeological Science 41:493501.
Lee S, Bronk Ramsey C. 2012. Development and application of the trapezoidal model for archaeological chronologies. Radiocarbon 54(1):107122.
Loftus E, Sealy J, Lee-Thorp J. 2016. New radiocarbon dates and Bayesian models for Nelson Bay Cave and Byneskranskop 1: implications for the South African Later Stone Age Sequence. Radiocarbon 58(02):365381.
MacDonald GM, Beilman DW, Kremenetski KV, Sheng Y, Smith LC, Velichko AA. 2006. Rapid early development of circumarctic peatlands and atmospheric CH4 and CO2 variations. Science 314(5797):285288.
Molak M, Suchard MA, Ho SYW, Beilman DW, Shapiro B. 2015. Empirical calibrated radiocarbon sampler: a tool for incorporating radiocarbon-date and calibration error into Bayesian phylogenetic analyses of ancient DNA. Molecular Ecology Resources 15(1):8186.
Needham S, Bronk Ramsey C, Coombs D, Cartwright C, Pettitt PB. 1998. An independent chronology for British Bronze Age metalwork: the results of the Oxford Radiocarbon Accelerator Programme. Archaeological Journal 154:55107.
Parzen E. 1962. On estimation of a probability density function and mode. Ann. Math. Statist 33(3):10651076.
Rasmussen SO, Andersen KK, Svensson AM, Steffensen JP, Vinther BM, Clausen HB, Siggaard-Andersen ML, Johnsen SJ, Larsen LB, Dahl-Jensen D, Bigler M, R̈othlisberger R, Fischer H, Goto-Azuma K, Hansson ME, Ruth U. 2006. A new Greenland ice core chronology for the last glacial termination. Journal of Geophysical Research 111.
Reimer PJ, Bard E, Bayliss A, Beck JW, Blackwell PG, Bronk Ramsey C, Grootes PM, Guilderson TP, Haflidason H, Hajdas I, Hatte C, Heaton TJ, Hoffmann DL, Hogg AG, Hughen KA, Kaiser KF, Kromer B, Manning SW, Niu M, Reimer RW, Richards DA, Scott EM, Southon JR, Staff RA, Turney CSM, van der Plicht J. 2013. IntCal13 and Marine13 radiocarbon age calibration curves 0–50,000 years cal BP. Radiocarbon 55(4):18691887.
Rosenblatt M. 1956. Remarks on some nonparametric estimates of a density function. Ann. Math. Statist 27(3):832837.
Rubin DB. 1981. The Bayesian Bootstrap. The Annals of Statistics 9(1):130134.
Shennan S. 2013. Demographic continuities and discontinuities in Neolithic Europe: evidence, methods and implications. Journal of Archaeological Method and Theory 20(2):300311.
Silverman BW. 1986. Density Estimation for Statistics and Data Analysis. Volume 26. CRC Press.
Stuart AJ, Kosintsev P, Higham T, Lister AM. 2004. Pleistocene to Holocene extinction dynamics in giant deer and woolly mammoth. Nature 431(7009):684689.
Svensson A, Andersen KK, Bigler M, Clausen HB, Dahl-Jensen D, Davies S, Johnsen SJ, Muscheler R, Parrenin F, Rasmussen SO, et al. 2008. A 60 000 year Greenland stratigraphic ice core chronology. Climate of the Past 4(1):4757.
Timpson A, Colledge S, Crema E, Edinborough K, Kerig T, Manning K, Thomas MG, Shennan S. 2014. Reconstructing regional population fluctuations in the European Neolithic using radiocarbon dates: a new case-study using an improved method. Journal of Archaeological Science 52:549557.
Ukkonen P, Aaris-Sørensen K, Arppe L, Clark P, Daugnora L, Lister A. Lõugas L, Seppa H, Sommer R, Stuart A, et al. 2011. Woolly mammoth (Mammuthus primigenius Blum.) and its environment in northern Europe during the last glaciation. Quaternary Science Reviews 30(5):693712.
Williams NA. 2012. The use of summed radiocarbon probability distributions in archaeology: a review of methods. Journal of Archaeological Science 39(3):578589.
Zhang X, King ML, Hyndman RJ. 2006. A Bayesian approach to bandwidth selection for multivariate kernel density estimation. Computational Statistics & Data Analysis 50(11):30093031.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0033-8222
  • EISSN: 1945-5755
  • URL: /core/journals/radiocarbon
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 5
Total number of PDF views: 47 *
Loading metrics...

Abstract views

Total abstract views: 146 *
Loading metrics...

* Views captured on Cambridge Core between 20th November 2017 - 17th December 2017. This data will be updated every 24 hours.