1. bookVolume 40 (2013): Issue 2 (June 2013)
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eISSN
1897-1695
First Published
04 Jul 2007
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1 time per year
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English
access type Open Access

A coarse Bayesian approach to evaluate luminescence ages

Published Online: 16 Mar 2013
Volume & Issue: Volume 40 (2013) - Issue 2 (June 2013)
Page range: 90 - 100
Journal Details
License
Format
Journal
eISSN
1897-1695
First Published
04 Jul 2007
Publication timeframe
1 time per year
Languages
English
Abstract

This paper develops a simplified Bayesian approach to evaluate a luminescence age. We limit our purpose to the cause-effect relationship between the age and the accumulated dose. The accumulated dose is given as a function of the age and several others parameters: internal radionuclides contents, gamma dose rate, cosmic dose rate, alpha efficiency, wetness, conversion factors, wetness coefficients, fading rate and storage time. The age is the quantity we are looking for. Bayes’ theorem expresses the changes on the probability distribution of age due to the luminescence study. The information before study (prior) comprises what is previously known about the age and the archaeological model (cultural period, stratigraphic relations, type, etc.) as well as the parameters of the physical model. The accumulated dose consists in the data describing the measurement. The various stages of Bayesian approach were implemented using the software WinBugs. Simulated data sets were used in various models. We present various small models representing typical examples encountered in luminescence dating.

Keywords

[1] Adamiec G and Aitken MJ, 1998. Dose-rate conversion factors: update. Ancient TL 16: 37–50. Search in Google Scholar

[2] Aitken MJ, 1985. Thermoluminescence dating, Studies in Archaeological Science. Academic press, London. Search in Google Scholar

[3] Aitken MJ, 1998. An introduction to Optical dating — The dating of quaternary sediments by the use of photon-stimulated luminescence. Oxford Science Publication. Oxford University Press, Oxford. Search in Google Scholar

[4] Box GEP, 1980. Sampling and Bayes’ Inference in Scientific Modelling and Robustness. Journal of the Royal Statistical Society. Series A (General) 143: 383. http://dx.doi.org/10.2307/298206310.2307/2982063Search in Google Scholar

[5] Brooks S, Gelman A, Jones GL and Meng X-L (Eds.), 2011. Handbook of Markov Chain Monte Carlo — CRC Press Book. Chapman & Hall/CRC Handbooks of Modern Statistical Methods. CRC Press. Search in Google Scholar

[6] Buck CE and Millard AR (Eds.), 2004. Tools for Constructing Chronologies, 1st ed, Lecture Note in Statistics. Springer, London. 10.1007/978-1-4471-0231-1_1Search in Google Scholar

[7] Buck CE, Cavanagh WG and Litton CD, 1996. Bayesian approach to interpreting archaeological data, Statistics in Practice. John Wiley & Sons, Inc., Chichester. Search in Google Scholar

[8] Clark-Balzan LA, Candy I, Schwenninger J-L, Bouzouggar A, Blockley S, Nathan R and Barton RNE, 2012. Coupled U-series and OSL dating of a Late Pleistocene cave sediment sequence, Morocco, North Africa: Significance for constructing Palaeolithic chronologies. Quaternary Geochronology 12: 53–64, DOI 10.1016/j.quageo.2012.06.006. http://dx.doi.org/10.1016/j.quageo.2012.06.00610.1016/j.quageo.2012.06.006Search in Google Scholar

[9] Cox RT, 1946. Probability, Frequency, and Reasonable Expectation. American Journal of Physics 14: 1–13, DOI 10.1119/1.1990764. http://dx.doi.org/10.1119/1.199076410.1119/1.1990764Search in Google Scholar

[10] Gelman A and Shalizi CR, 2012. Philosophy and the practice of Bayesian statistics. British Journal of Mathematical and Statistical Psychology. 10.1093/oxfordhb/9780195392753.013.0011Search in Google Scholar

[11] Gelman A and Shirley K, 2011. Inference from simulations and monitoring convergence, in: Brooks S, Gelman A, Jones GL and Meng X-L (Eds.), Handbook of Markov Chain Monte Carlo — CRC Press Book, Chapman & Hall/CRC Handbooks of Modern Statistical Methods. CRC Press, pp. 163–174. 10.1201/b10905-7Search in Google Scholar

[12] Huntley DJ and Lamothe M, 2001. Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating. Canadian Journal of Earth Sciences 38(7): 1093–1106, DOI 10.1139/e01-013. http://dx.doi.org/10.1139/e01-01310.1139/e01-013Search in Google Scholar

[13] Huntriss A, 2008. A Bayesian analysis of luminescence dating. PhD, University of Durham. Search in Google Scholar

[14] Kerman J and Gelman A, 2006. Bayesian Data Analysis using R. Rnews 6: 21–24. Search in Google Scholar

[15] Lanos P, 2004. Bayesian inference of calibration curves: Application to Archaeomagnetism, in: Buck CE and Millard AR (Eds.), Tools for Constructing Chronologies, Lecture Note in Statistics. Springer, London, pp. 43–82. http://dx.doi.org/10.1007/978-1-4471-0231-1_310.1007/978-1-4471-0231-1_3Search in Google Scholar

[16] Lunn D, Spiegelhalter D, Thomas A and Best N, 2009. The BUGS project: Evolution, critique and future directions. Statistics in Medicine 28(25): 3049–3067, DOI 10.1002/sim.3680. http://dx.doi.org/10.1002/sim.368010.1002/sim.368019630097Search in Google Scholar

[17] Millard AR, 2004. Taking Bayes beyond radiocarbon: Bayesian approaches to some other chronometric methods, in: Buck, CE, Millard AR (Eds.), Tools for Constructing Chronologies, Lecture Note in Statistics. Springer, London, pp. 231–248. http://dx.doi.org/10.1007/978-1-4471-0231-1_1110.1007/978-1-4471-0231-1_11Search in Google Scholar

[18] Millard AR, 2006a. Bayesian analysis of pleistocene chronometric methods. Archaeometry 48(2): 359–375, DOI 10.1111/j.1475-4754.2006.00261.x. http://dx.doi.org/10.1111/j.1475-4754.2006.00261.x10.1111/j.1475-4754.2006.00261.xSearch in Google Scholar

[19] Millard AR, 2006b. Bayesian analysis of ESR dates, with application to Border Cave. Quaternary Geochronology 1(2): 159–166, DOI 10.1016/j.quageo.2006.03.002. http://dx.doi.org/10.1016/j.quageo.2006.03.00210.1016/j.quageo.2006.03.002Search in Google Scholar

[20] Murray AS and Wintle AG, 2003. The single aliquot regenerative dose protocol: potential for improvements in reliability. Radiation Measurements 37(4–5): 377–381, DOI 10.1016/S1350-4487(03)00053-2. http://dx.doi.org/10.1016/S1350-4487(03)00053-210.1016/S1350-4487(03)00053-2Search in Google Scholar

[21] Nicholls G and Jones M, 2001. Radiocarbon dating with temporal order constraints. Journal of the Royal Statistical Society: Series C (Applied Statistics) 50(4): 503–521, DOI 10.1111/1467-9876.00250. http://dx.doi.org/10.1111/1467-9876.0025010.1111/1467-9876.00250Search in Google Scholar

[22] Orton C, 1980. Mathematics in Archaeology. 1st ed, Collins archaeolgy. Wiliams Collins Sons & Co, London. Search in Google Scholar

[23] Popper K, 1982. La logique de la découverte scientifique (The logic of scientific discovery). 2nd French ed. Payot, Paris (in French). Search in Google Scholar

[24] Prescott JR and Hutton JT, 1994. Cosmic ray contributions to dose rates for luminescence and ESR dating: large depths and long-term time variations. Radiation Measurements 23(2–3): 497–500, DOI 10.1016/1350-4487(94)90086-8,. http://dx.doi.org/10.1016/1350-4487(94)90086-810.1016/1350-4487(94)90086-8Search in Google Scholar

[25] Preusser F, Degering D, Fuchs M, Hilgers A, Kadereit A, Klasen N, Krbetschek M, Richter D and Spencer JQG, 2008. Luminescence dating: basics, methods and applications. Quaternary Science Journal 57(1–2): 95–149, DOI 10.3285/eg.57.1-2.5. 10.3285/eg.57.1-2.5Search in Google Scholar

[26] R Development Core Team, 2009. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, WEB site: <http://www.R-project.org>. Accessed 2010 April 14. Search in Google Scholar

[27] Rhodes EJ, Bronk Ramsey C, Outram Z, Batt C, Willis L, Dockrill S and Bond J, 2003. Bayesian methods applied to the interpretation of multiple OSL dates: high precision sediment ages from Old Scatness Broch excavations, Shetland Isles. Quaternary Science Reviews 22(10–13): 1231–1244, DOI 10.1016/S0277-3791(03)00046-5. http://dx.doi.org/10.1016/S0277-3791(03)00046-510.1016/S0277-3791(03)00046-5Search in Google Scholar

[28] Sivia DS, Burbidge C, Roberts RG and Bailey RM, 2004. A Bayesian approach to the evaluation of equivalent doses in sediment mixtures for luminescence dating, in: AIP Conference Proceedings. p. 305. http://dx.doi.org/10.1063/1.183522710.1063/1.1835227Search in Google Scholar

[29] Sommer KD and Siebert BRL, 2006. Systematic approach to the modelling of measurements for uncertainty evaluation. Metrologia 43(4): S200–S210, DOI 10.1088/0026-1394/43/4/S06. http://dx.doi.org/10.1088/0026-1394/43/4/S0610.1088/0026-1394/43/4/S06Search in Google Scholar

[30] Spiegelhalter D, Thomas A, Best N and Gilks W, 1996. BUGS 0.5: Bayesian inference using Gibbs sampling manual (version ii). MRC Biostatistics Unit, Institute of Public Health, Cambridge, UK. Search in Google Scholar

[31] Steel D, 2001. Bayesian statistics in radiocarbon calibration. Philisophy of Sciences 68(3): S153–S164. http://dx.doi.org/10.1086/39290510.1086/392905Search in Google Scholar

[32] Van Strydonck M, Moor AD and Benazeth D, 2004. 14C dating compared to art historical dating of roman and coptic textiles from egypt. Radiocarbon 46: 231–244. 10.1017/S0033822200039552Search in Google Scholar

[33] Wintle AG, 1973. Anomalous Fading of Thermoluminescence in Mineral Samples. Nature 245: 143–144, DOI 10.1038/245143a0. http://dx.doi.org/10.1038/245143a010.1038/245143a0Search in Google Scholar

[34] Wintle AG, 2008. Luminescence dating of Quaternary sediments — Introduction. Boreas 37(4): 469–470, DOI 10.1111/j.1502-3885.2008.00060.x. http://dx.doi.org/10.1111/j.1502-3885.2008.00060.x10.1111/j.1502-3885.2008.00060.xSearch in Google Scholar

[35] Zimmerman DW, 1971. Thermoluminescent Dating Using Fine Grains from Pottery. Archaeometry 13(1), 29–52, DOI 10.1111/j.1475-4754.1971.tb00028.x. http://dx.doi.org/10.1111/j.1475-4754.1971.tb00028.x10.1111/j.1475-4754.1971.tb00028.xSearch in Google Scholar

[36] Zink A, 2008. Uncertainties on the Luminescence Ages and Anomalous Fading. Geochronometria 32: 47–50, DOI 10.2478/v10003-008-0027-4. http://dx.doi.org/10.2478/v10003-008-0027-410.2478/v10003-008-0027-4Search in Google Scholar

[37] Zink A, 2009. Luminescence date and archaeological ages: An epistemology of the luminescence dating. in: Cavulli F, Prudêncio MI, DIAS MI (Eds.), Defining a Methodological Approach to Interpret Structural Evidence; Archaeometry, British Archaeological Report. Presented at the XV UISPP World Congress (Lisbon, 4–9 September 2006) / XV Congrès Mondial (Lisbonne, 4–9 Septembre 2006, Vol 32, Sessions WS28, C69, C70 and C71., Archaeopress, pp. 113–116. Search in Google Scholar

[38] Zink A and Porto E, 2005. Luminescence dating of the Tanagra terracottas of the Louvre collections. Geochronometria 24: 21–26. Search in Google Scholar

[39] Zink AJC, Dabis S, Porto E and Castaing J, 2010. Alpha efficiency under TL and OSL — A subtraction technique using OSL and TL to detect artificial irradiation. Radiation Measurements 45(3–6): 649–652, DOI 10.1016/j.radmeas.2010.01.017. http://dx.doi.org/10.1016/j.radmeas.2010.01.01710.1016/j.radmeas.2010.01.017Search in Google Scholar

[40] Zink AJC and Porto E, submitted. Bayesian Approach or Robust Bayesian analysis? Quaternary Geochronology. Search in Google Scholar

[41] Zink AJC, Porto E, Genevey A, Gallet Y, Rante R and Collinet A, submitted. Absolute chronology of Nishapur’s Citadel (Iran). Contribution of luminescence dating and archaeomagnetic analysis. Quaternary Geochronology. Search in Google Scholar

[42] Zink AJC, Susino GJ, Porto E and Huffman TN, 2012. Direct OSL dating of Iron Age pottery from South Africa — Preliminary dosimetry investigations. Quaternary Geochronology 8: 1–9, DOI 10.1016/j.quageo.2011.11.008. http://dx.doi.org/10.1016/j.quageo.2011.11.00810.1016/j.quageo.2011.11.008Search in Google Scholar

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