Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-13T02:22:32.819Z Has data issue: false hasContentIssue false

Pushing the Limits of AMS Radiocarbon Dating with Improved Bayesian Data Analysis

Published online by Cambridge University Press:  18 July 2016

V Palonen*
Affiliation:
Accelerator Laboratory, PO Box 43, FIN-00014 University of Helsinki, Finland
P Tikkanen
Affiliation:
Accelerator Laboratory, PO Box 43, FIN-00014 University of Helsinki, Finland
*
Corresponding author. Email: vesa.palonen@helsinki.fi
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.

We present an improved version of the continuous autoregressive (CAR) model, a Bayesian data analysis model for accelerator mass spectrometry (AMS). Measurement error is taken to be Poisson-distributed, improving the analysis for samples with only a few counts. This, in turn, enables pushing the limit of radiocarbon measurements to lower concentrations. On the computational side, machine drift is described with a vector of parameters, and hence the user can examine the probable shape of the trend. The model is compared to the conventional mean-based (MB) method, with simulated measurements representing a typical run of a modern AMS machine and a run with very old samples. In both comparisons, CAR has better precision, gives much more stable uncertainties, and is slightly more accurate. Finally, some results are given from Helsinki AMS measurements of background sample materials, with natural diamonds among them.

Type
Articles
Copyright
Copyright © 2007 by the Arizona Board of Regents on behalf of the University of Arizona 

References

Broemeling, LD, Cook, P. 1997. A Bayesian analysis of regression models with continuous errors with application to longitudinal studies. Statistics in Medicine 16:(4)321–2.Google Scholar
Brooks, SP, Gelman, A. 1998. General methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics 7(4):434–55.Google Scholar
Gelman, A, Rubin, DB. 1992. Inference from iterative simulation using multiple sequences. Statistical Science 7(4):457511.Google Scholar
Gelman, A, Carlin, JB, Stern, HS, Rubin, DB. 2003. Bayesian Data Analysis. 2nd edition. Boca Raton: Chapman & Hall/CRC. 668 p.CrossRefGoogle Scholar
Gilks, WR, Richardson, S, Spiegelhalter, DJ, editors. 1996. Markov Chain Monte Carlo in Practice. Boca Raton: Chapman & Hall/CRC.Google Scholar
Jaynes, ET. 2003. Probability Theory: The Logic of Science. Cambridge: Cambridge University Press. 758 p.CrossRefGoogle Scholar
Jensen, FV. 1996. An Introduction to Bayesian Networks. London: UCL Press. 178 p.Google Scholar
Jones, RH. 1993. Longitudinal Data with Serial Correlations: A State-Space Approach. London: Chapman & Hall/CRC. 240 p.CrossRefGoogle Scholar
Kass, RE, Wasserman, L. 1994. Formal rules for selecting prior distributions: a review and annotated bibliography. Technical report #583, Carnegie Mellon University, Pennsylvania, USA.Google Scholar
Palonen, V, Tikkanen, P. 2007a. An information-efficient Bayesian model for AMS data analysis. Radiocarbon 49(2):369–77.Google Scholar
Palonen, V, Tikkanen, P. 2007b. A shot at a Bayesian model for data analysis in AMS measurements. Nuclear Instruments and Methods in Physics Research B 259(3):154–7.Google Scholar
Palonen, V, Tikkanen, P, Keinonen, J. 2004. Ion-optical modelling of the Helsinki AMS tandem. Nuclear Instruments and Methods in Physics Research B 223–224:227–32.CrossRefGoogle Scholar
Särkkä, S, Vehtari, A. 1999. MCMC diagnostics toolbox for MATLAB [software]. URL: http://www.lce.hut.fi/research/mm/mcmcdiag/.Google Scholar
Sivia, DS. 1996. Data Analysis: A Bayesian Tutorial. Oxford: Clarendon Press. 240 p.Google Scholar
Smith, BJ. 2005. Bayesian Output Analysis (BOA) program, version 1.1.5 [software]. URL: http://www.public-health.uiowa.edu/boa.Google Scholar
Tikkanen, P, Palonen, V, Jungner, H, Keinonen, J. 2004. AMS facility at the University of Helsinki. Nuclear Instruments and Methods in Physics Research B 223–224:35–9.CrossRefGoogle Scholar