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Formal Statistical Models for Estimating Radiocarbon Calibration Curves

  • C E Buck (a1) and P G Blackwell (a1)

Abstract

We report on the development and implementation of a model-based statistical method for the estimation of radiocarbon calibration curves using diverse data. The method takes account of uncertainty on both the 14C and calendar scales, coherently integrating data, the calendar age estimates of which arise from different dating methods. It also allows for correlation between observations, if they have particular sources of uncertainty in common. We adopt an approach based on a random walk model, tailoring it to take account of possible calendar age offsets between different data sources by adding a random effect component. The latter allows us to use the same modeling framework for constructing the new calibration curve IntCal04, the comparison curve NotCal04, the Southern Hemisphere curve SHCal04, and the marine calibration curve Marine04.

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Copyright

Corresponding author

Corresponding author. Email: c.e.buck@sheffield.ac.uk.

References

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Christen, JA, Nicholls, G. 2000. Random-walk radiocarbon calibration. Technical report #457. Auckland: Mathematics Department, University of Auckland.
Goméz Portugal Aguilar, D, Litton, CD, O'Hagan, A. 2002. Novel statistical model for a piece-wise linear radiocarbon calibration curve. Radiocarbon 44(1): 195212.
Hughen, KA, Baillie, MGL, Bard, E, Bayliss, A, Beck, JW, Blackwell, PG, Buck, CE, Burr, GS, Cutler, KB, Damon, PE, Edwards, RL, Fairbanks, RG, Friedrich, M, Guilderson, TP, Herring, C, Kromer, B, McCormac, G, Manning, S, Bronk Ramsey, C, Reimer, PJ, Reimer, RW, Remmele, S, Southon, JR, Stuiver, M, Talamo, S, Taylor, FW, van der Plicht, J, Weyhenmeyer, CE. 2004. Marine04 marine radiocarbon age calibration, 0–26 cal kyr B P. Radiocarbon, this issue.
Knox, FB, McFadgen, BG. 1997. Least-squares fitting a smooth curve to radiocarbon calibration data. Radiocarbon 39(2):193204.
McCormac, G, Hogg, AG, Blackwell, PG, Buck, CE, Higham, TFG, Reimer, PJ. 2004. SHCal04 Southern Hemisphere calibration, 0–11.0 cal kyr BP. Radiocarbon, this issue.
Reimer, PJ, Baillie, MGL, Bard, E, Bayliss, A, Beck, JW, Blackwell, PG, Buck, CE, Burr, GS, Cutler, KB, Damon, PE, Edwards, RL, Fairbanks, RG, Friedrich, M, Guilderson, TP, Herring, C, Hughen, KA, Kromer, B, McCormac, G, Manning, S, Bronk Ramsey, C, Reimer, RW, Remmele, S, Southon, JR, Stuiver, M, Talamo, S, Taylor, FW, van der Plicht, J, Weyhenmeyer, CE. 2004. IntCal04 terrestrial radiocarbon age calibration, 0–26 cal kyr BP. Radiocarbon, this issue.
Stuiver, M, Reimer, PJ, Bard, E, Beck, JW, Burr, GS, Hughen, KA, Kromer, B, McCormac, FG, van der Plicht, J, Spurk, M. 1998. IntCal98 radiocarbon age calibration, 24,000–0 cal BP. Radiocarbon 40(3):1041–83.
van der Plicht, J, Beck, JW, Bard, E, Baillie, MGL, Blackwell, PG, Buck, CE, Friedrich, M, Guilderson, TP, Hughen, KA, Kromer, B, McCormac, FG, Bronk Ramsey, C, Reimer, PJ, Reimer, RW, Remmele, S, Richards, DA, Southon, JR, Stuiver, M, Weyhenmeyer, CE. 2004. NotCal04–comparison/calibration 14C records 26–50 cal kyr BP. Radiocarbon, this issue.
Ward, GK, Wilson, SR. 1978. Procedures for comparing and combining radiocarbon age determinations: a critique. Archaeometry 20(1):1931.
West, M, Harrison, PJ. 1997. Bayesian Forecasting and Dynamic Models. 2nd edition. New York: Springer-Verlag.

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