Hostname: page-component-7f64f4797f-tldsr Total loading time: 0.001 Render date: 2025-11-04T01:44:43.533Z Has data issue: false hasContentIssue false
  • English
  • Français

A New Robust Statistical Model for Radiocarbon Data

Published online by Cambridge University Press:  18 July 2016

J Andrés Christen  and
Sergio Pérez E
J Andrés Christen*
Affiliation:
Centro de Investigaciön en Matemáticas, A. C. (CIMAT), A.P. 402, Guanajuato, Guanajuato 36000, Mexico
Sergio Pérez E
Affiliation:
Centro de Investigaciön en Matemáticas, A. C. (CIMAT), A.P. 402, Guanajuato, Guanajuato 36000, Mexico
*
Corresponding author. Email: sergiop@cimat.mx
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The general method currently used to analyze radiocarbon data (y) is conditional on the standard deviation (σ), reported by 14C laboratories, which reflects the uncertainty in the dating process. This uncertainty is measured through a series of empirical as well as theoretical considerations about the dating process, chemical preprocessing, etc. Nevertheless, σ is assumed as known in the statistical model for 14C data used since the dawn of the discipline. This paper proposes a method for the analysis of 14C data where the associated variance is taken as the product of an unknown constant α with the sum of the variance reported by the laboratory σ2 and the variance of the calibration curve σ2(θ) (that is, an unknown error multiplier). Using this approach, assuming that the 14C determination y arises from a Normal population and that, a priori, α has an inverse gamma distribution InvGa(a, b), the resulting dating model is a t distribution with 2a degrees of freedom. The introduction of parameters a and b allows a robust analysis in the presence of atypical data and at the same time incorporates the uncertainty associated with the intra- and interlaboratory error assessment processes. Comparisons with the common Normal model show that the proposed t model produces smoother posterior distributions and seem to be far more robust to atypical data, presenting a simpler alternative to the standard 14C outlier analysis. Moreover, this new model might be a step forward in understanding and explaining the otherwise elusive scatter in 14C data seen in interlaboratory studies.

Information

Type
Statistical Applications
Information
Radiocarbon , Volume 51 , Issue 3 , 2009 , pp. 1047 - 1059
Copyright
Copyright © 2009 by the Arizona Board of Regents on behalf of the University of Arizona 

References

REFERENCES

Berger, JO, Liseo, B, Wolpert, RL. 1999. Integrated likelihood methods for eliminating nuisance parameters (with discussion). Statistical Science 14(1):1–28.Google Scholar
Bernardo, JM. 1979. Reference posterior distributions for Bayesian inference. The Journal of the Royal Statistical Society B 41(2):113–47.Google Scholar
Bernardo, JM. 2005. Reference analysis. In: Dey, DK, Rao, CR, editors. Handbook of Statistics 25. Amsterdam: Elsevier. p 17–90.Google Scholar
Blaauw, M, Christen, JA. 2005. Radiocarbon peat chronologies and environmental change. Applied Statistics 54(5):805–16.Google Scholar
Blaauw, M, Christen, JA, Guilderson, TP, Reimer, PJ, Brown, TA. 2005. The problems of radiocarbon dating. Science 308(5728):1551–3.Google Scholar
Blaauw, M, Bakker, R, Christen, JA, Hall, VA, van der Plicht, J. 2007. A Bayesian framework for age modeling of radiocarbon-dated peat deposits: case studies from the Netherlands. Radiocarbon 49(2):357–67.CrossRefGoogle Scholar
Buck, CE, Blackwell, PG. 2004. Formal statistical models for estimating radiocarbon calibration curves. Radiocarbon 46(3):1093–102.Google Scholar
Buck, CE, Christen, JA, James, GN. 1999. BCal: an on-line Bayesian radiocarbon calibration tool. Internet Archaeology 7. Available at http://intarch.ac.uk/journal/issue7/buck_index.html.Google Scholar
Buck, CE, Higham, TFG, Lowe, DJ. 2003. Bayesian tools for tephrochronology. The Holocene 13(5):639–47.Google Scholar
Buck, CE, Goméz Portugal, D, Litton, CD, O'Hagan, A. 2006. Bayesian non-parametric estimation of the calibration curve for radiocarbon dating. Bayesian Analysis 1(2):265–88.Google Scholar
Chen, MH, Shao, QM. 1999. Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics 8(1):69–92.Google Scholar
Christen, JA. 1994. Summarizing a set of radiocarbon determinations: a robust approach. Applied Statistics-Journal of the Royal Statistical Society Series C 43(3):489–503.Google Scholar
Clark, R. 1975. A calibration curve for radiocarbon dates. Antiquity 49(196):251–66.CrossRefGoogle Scholar
Damon, PE, Donahue, DJ, Gore, BH, Hatheway, AL, Jull, AJT, Linick, TW, Sercel, PJ, Toolin, LJ, Bronk, CR, Hall, ET, Hedges, REM, Housley, R, Law, IA, Perry, C, Bonani, G, Trumbore, S, Ambers, JC, Bowman, SGE, Leese, MN, Tite, MS. 1989. Radiocarbon dating of the Shroud of Turin. Nature 337(6208):611–5.CrossRefGoogle Scholar
Gibbons, JD, Chakraborti, S. 2003. Nonparametric Statistical Inference. Boca Raton: CRC Press. 4th edition. 306 p.Google Scholar
Naylor, JC, Smith, AFM. 1988. An archaeological inference problem. Journal of the American Statistical Association 83(403):588–95.Google Scholar
Reimer, PJ, Baillie, MGL, Bard, E, Bayliss, A, Beck, JW, Bertrand, CJH, Blackwell, PG, Buck, CE, Burr, GS, Cutler, KB, Damon, PE, Edwards, RL, Fairbanks, RG, Friedrich, M, Guilderson, TP, Hogg, AG, 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 46(3):1029–58.Google Scholar
Scott, EM. 2003. Section 10: Summary and Conclusions. In: The Third International Radiocarbon Intercomparison (TIRI) and the Fourth International Radiocarbon (FIRI), 1990–2002. Results, Analysis and Conclusions. Radiocarbon 45(2):285–91.Google Scholar
Ward, GK, Wilson, SR. 1978. Procedures for comparing and combining radiocarbon age determinations: a critique. Archaeometry 20(1):19–31.Google Scholar