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Novel Statistical Model for a Piece-Wise Linear Radiocarbon Calibration Curve

Published online by Cambridge University Press:  18 July 2016

Delil Gómez Portugal Aguilar ,
Cliff D Litton  and
Anthony O'Hagan
Delil Gómez Portugal Aguilar*
Affiliation:
Department of Probability and Statistics, University of Sheffield, Sheffield S3 7RH, United Kingdom
Cliff D Litton
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
Anthony O'Hagan
Affiliation:
Department of Probability and Statistics, University of Sheffield, Sheffield S3 7RH, United Kingdom
*
Corresponding author. Email: [email protected].
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Abstract

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The process of calibrating radiocarbon determinations onto the calendar scale requires the setting of a specific statistical model for the calibration curve. This model specification will bear fundamental importance for the resulting inference regarding the parameter of interest—namely, in general, the calendar age associated to the sample that has been 14C-dated.

Traditionally, the 14C calibration curve has been modelled simply as the piece-wise linear curve joining the (internationally agreed) high-precision calibration data points; or, less frequently, by proposing spline functions in order to obtain a smoother curve.

We present a model for the 14C calibration curve which, based on specific characteristics of the dating method, yields a piece-wise linear curve, but one which rather than interpolating the data points, smooths them. We show that with this specific model if a piece-wise linear curve is desired, an underlying random walk model is implied as covariance structure (and vice versa). Furthermore, by making use of all the information provided by the calibration data in a comprehensive way, we achieve an improvement over current models by getting more realistic variance values for the calibration curve.

Type
Notes and Technical Comments
Information
Radiocarbon , Volume 44 , Issue 1 , 2002 , pp. 195 - 212
Copyright
Copyright © 2002 by the Arizona Board of Regents on behalf of the University of Arizona 

References

Aitken, MJ. 1990. Science-based dating in archaeology. London: Longman Archaeology Series.Google Scholar
Bowman, S. 1990. Radiocarbon dating (Interpreting the past). London: British Museum Publications Ltd.Google Scholar
Bowman, SGE, Leese, MN. 1995. Radiocarbon calibration: current issues. American Journal of Archaeology 99(1):102–5.Google Scholar
Bronk Ramsey, C. 1995. Radiocarbon calibration and analysis of stratigraphy: the OxCal program. Radiocarbon 37(2):425–30.CrossRefGoogle Scholar
Buck, CE, Cavanagh, WG, Litton, CD. 1996. Bayesian approach to interpreting archaeological data. Chichester: John Wiley & Sons.Google Scholar
Buck, CE, Litton, CD, Scott, EM. 1994. Making the most of 14C dating: some statistical considerations. Antiquity 68:252–63.CrossRefGoogle Scholar
Christen, JA. 1994. Bayesian interpretation of radiocarbon results. PhD thesis. University of Nottingham.Google Scholar
Christen, JA, Litton, CD. 1995. A Bayesian approach to wiggle-matching. Journal of Archaeological Science 22:719–25.Google Scholar
Gillespie, R. 1984. Radiocarbon user's handbook. Oxford University. Committee for Archaeology. Monograph Number 3.Google Scholar
Grimmett, GR, Stirzaker, DR. 1992. Probability and random processes. Second edition. Oxford Science Publications. Clarendon Press, Oxford.Google Scholar
Knox, FB, McFadgen, BG. 1997. Least-squares fitting a smooth curve to radiocarbon calibration data. Radiocarbon 39(2):193–204.CrossRefGoogle Scholar
McCormac, FG, Baillie, MGL. 1993. Radiocarbon to calendar date conversion: calendrical band widths as a function of 14C precision. Radiocarbon 35(2):311–6.Google Scholar
Naylor, JC, Smith, AMF. 1988. An archaeological inference problem. Journal of the American Statistical Association 83(403):588–95.Google Scholar
Neal, RM. 1999. Regression and classification using Gaussian process priors. In: Bernardo, JM, Berger, JO, Dawid, AP, Smith, AFM, editors. Bayesian statistics 6. Oxford University Press. p 69–95.Google Scholar
Nicholls, G, Christen, JA. 2000. Random-walk 14C calibration. Technical report number 457. Mathematics Department, University of Auckland.Google Scholar
O'Hagan, A. 1992. Some Bayesian numerical analysis (with discussion). In: Bernardo, JM, Berger, JO, Dawid, A P, Smith, AFM, editors. Bayesian statistics 4. Oxford University Press. p 345–363.Google Scholar
O'Hagan, A. 1994. Kendall's advanced theory of statistics. Volume 2B, Bayesian inference. London: Edward Arnold.Google Scholar
O'Hagan, A, Kennedy, MC, Oakley, JE. 1999. Uncertainty analysis and other inference tools for complex computer codes (with discussion). In: Bernardo, JM, Berger, JO, Dawid, AP, Smith, AFM, editors. Bayesian statistics 6. Oxford University Press. p 503–24.Google Scholar
Pazdur, MF, Michczynska, DJ. 1989. Improvement of the procedure for probabilistic calibration of 14C results. Radiocarbon 31(3):824–32.Google Scholar
Pearson, GW, Stuiver, M. 1986. High-precision calibration of the time scale, 500–2500 BC. Radiocarbon 28(2B):839–62.Google Scholar
Schmidt, AM, O'Hagan, A. 2000. Bayesian inference for nonstationary spatial covariance structure via spatial deformations. Research report no. 498/00. Department of Probability and Statistics, University of Sheffield.Google Scholar
Scull, C, Bayliss, A. 1999. Radiocarbon dating and Anglo-Saxon graves. In: von Freeden, Koch and Wieczorek, , editors. Volker an Nord- und Ostsee und die Franken.Google Scholar
Stuiver, M, Pearson, GW. 1986. High-precision calibration of the 14C time scale, AD 1950–500 BC. Radiocarbon 28(2B):805–38.Google Scholar
Stuiver, M, Reimer, P. 1989. Histograms obtained from computerized 14C age calibration. Radiocarbon 31(3):817–23.Google Scholar
Stuiver, M, Reimer, PJ. 1993. Extended 14C data base and revised CALIB 3.0 14C age calibration program. Radiocarbon 35(1):215–30.Google Scholar
Stuiver, M, Reimer, PJ, Bard, E, Beck, JW, Burr, GS, Hughen, KA, Kromer, B, McCormac, G, van der Plicht, J, Spurk, M. 1998. INTCAL98 radiocarbon age calibration, 24,000–0 cal BP. Radiocarbon 40(3):1041–83.Google Scholar
Talma, AS, Vogel, JC. 1993. A simplified approach to calibrating 14C dates. Radiocarbon 35(2):317–22.Google Scholar
Taylor, RE. 1987. Radiocarbon dating. an archaeological perspective. Orlando: Academic Press.Google Scholar
van der Plicht, J, Mook, WG. 1989. Calibration of 14C ages by computer. Radiocarbon 31(3):805–16.CrossRefGoogle Scholar
van der Plicht, J. 1993. The Groningen radiocarbon calibration program. Radiocarbon 35(1):231–7.Google Scholar
Zeidler, JA, Buck, CE, Litton, CD. 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