Hostname: page-component-76d6cb85b7-mgxrv Total loading time: 0 Render date: 2026-07-20T15:23:49.343Z Has data issue: false hasContentIssue false
  • English
  • Français

Robust Bayesian Analysis, an Attempt to Improve Bayesian Sequencing

Published online by Cambridge University Press:  18 July 2016

Franz Weninger ,
Peter Steier ,
Walter Kutschera  and
Eva Maria Wild
Franz Weninger*
Affiliation:
Vienna Environmental Research Accelerator (VERA), Faculty of Physics, Isotope Research, University of Vienna, Währinger Straße 17, A-1090 Vienna, Austria
Peter Steier
Affiliation:
Vienna Environmental Research Accelerator (VERA), Faculty of Physics, Isotope Research, University of Vienna, Währinger Straße 17, A-1090 Vienna, Austria
Walter Kutschera
Affiliation:
Vienna Environmental Research Accelerator (VERA), Faculty of Physics, Isotope Research, University of Vienna, Währinger Straße 17, A-1090 Vienna, Austria
Eva Maria Wild
Affiliation:
Vienna Environmental Research Accelerator (VERA), Faculty of Physics, Isotope Research, University of Vienna, Währinger Straße 17, A-1090 Vienna, Austria
*
Corresponding author. Email: franz.weninger@univie.ac.at.
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.

Bayesian sequencing of radiocarbon dates deals with the problem that in most cases there does not exist an unambiguous way to define the so-called prior function, which represents information in addition to the result of the 14C measurements alone. However, a random choice of a particular prior function can lead to biased results. In this paper, “robust Bayesian analysis,” which uses a whole set of prior functions, is introduced as a more reliable method. The most important aspects of the mathematical foundation and of the practical realization of the method are described. As a general result, robust Bayesian analysis leads to higher accuracy, but paid for with reduced precision. Our investigations indicate that it seems possible to establish robust analysis for practical applications.

Information

Type
Calibration, Data Analysis, and Statistical Methods
Information
Radiocarbon , Volume 52 , Issue 3: 20th Int. Radiocarbon Conference Proceedings , 2010 , pp. 962 - 983
Copyright
Copyright © 2010 by the Arizona Board of Regents on behalf of the University of Arizona 

References

Berger, JO. 1994. An overview of robust Bayesian analysis. Test 3(1):5–124.CrossRefGoogle Scholar
Berger, JO. 2006. The case for objective Bayesian analysis. Bayesian Analysis 1(3):385–402.CrossRefGoogle Scholar
Bonani, G, Ivy, S, Hajdas, I, Niklaus, TR, Suter, M. 1994. AMS 14C age determinations of tissue, bone and grass samples from the Ötztal Ice Man. Radiocarbon 36(2):247–50.Google Scholar
Bronk Ramsey, C. 1995. Radiocarbon calibration and analysis of stratigraphy: the OxCal program. Radiocarbon 37(2):425–30.Google Scholar
Bronk Ramsey, C. 2000. Comment on ‘The use of Bayesian statistics for 14C dates of chronologically ordered samples: a critical analysis.’ Radiocarbon 42(2):199–202.Google Scholar
Bronk Ramsey, C. 2001. Development of the radiocarbon calibration program. Radiocarbon 43(2A):355–63.Google Scholar
Bronk Ramsey, C. 2009. Bayesian analysis of radiocarbon dates. Radiocarbon 51(1):337–60.Google Scholar
Buck, CE, Kenworthy, JB, Litton, CD, Smith, AFM. 1991. Combining archaeological and radiocarbon information: a Bayesian approach to calibration. Antiquity 65(249):808–21.Google Scholar
Buck, CE, Litton, CD, Smith, AFM. 1992. Calibration of radiocarbon results pertaining to related archaeological results. Journal of Archaeological Science 19(5):497–512.Google Scholar
Buck, CE, Cavanagh, WG, Litton, CD. 1996. Bayesian Approach to Interpreting Archaeological Data. Chichester: John Wiley & Sons Ltd.Google Scholar
Garcia-Donato, G, Chen, M-H. 2005. Calibrating Bayes factor under prior predictive distributions. Statistica Sinica 15:359–80.Google Scholar
Gilks, WR, Richardson, S, Spiegelhalter, DJ, editors. 1996. Markov Chain Monte Carlo in Practice. London: Chapman & Hall.Google Scholar
Hedges, REM, Housley, RA, Bronk, CR, van Klinken, GJ. 1992. Radiocarbon dates from the Oxford AMS system: Archaeometry Datelist 15. Archaeometry 34(2):337–57.Google Scholar
Hoeting, JA, Madigan, D, Raftery, AE, Volinsky, CT. 1999. Bayesian model averaging: a tutorial. Statistical Science 14(4):382–401.Google Scholar
Jeffreys, H. 1961. Theory of Probability. London: Oxford University Press.Google Scholar
Jones, MD, Nicholls, GK. 2002. New radiocarbon calibration software. Radiocarbon 44(3):663–74.Google Scholar
Krause, A. 1994. Computerintensive statistische Methoden: Gibbs sampling in Regressionsmodellen. Stuttgart: Gustav Fischer Verlag. In German.Google Scholar
Kutschera, W, Müller, W. 2003. “Isotope language” of the Alpine Iceman investigated with AMS and MS. Nuclear Instruments and Methods in Physics Research B 204:705–19.Google Scholar
Kutschera, W, Rom, W. 2000. Ötzi, the prehistoric Iceman. Nuclear Instruments and Methods in Physics Research B 164–165:12–22.Google Scholar
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 B.C. Science 312(5773):565–9.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
Rios Insua, D, Ruggeri, F. 2000. Robust Bayesian Analysis. New York: Springer.CrossRefGoogle Scholar
Rom, W, Golser, R, Kutschera, W, Priller, A, Steier, P, Wild, EM. 1999. AMS 14C dating of equipment from the Iceman and of spruce logs from the prehistoric salt mines of Hallstatt. Radiocarbon 41(2):183–97.Google Scholar
Sivia, DS. 1996. Data Analysis—A Bayesian Tutorial. New York: Oxford University Press.Google Scholar
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.CrossRefGoogle Scholar
Steier, P, Rom, W, Puchegger, S. 2001. New methods and critical aspects in Bayesian mathematics for 14C calibration. Radiocarbon 43(2A):373–80.Google Scholar
Weninger, F, Steier, P, Kutschera, W, Wild, EM. 2006. The Principle of the Bayesian Method. Egypt and the Levant 16:317–24.Google Scholar