Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Event date model: a robust Bayesian tool for chronology building

  • Philippe, Lanos (IRAMAT-CRPAA, Universite Bordeaux-Montaigne and Geosciences-Rennes) ;
  • Anne, Philippe (Laboratoire de mathematiques Jean Leray, Universite Nantes)
  • Received : 2017.07.07
  • Accepted : 2018.01.10
  • Published : 2018.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

We propose a robust event date model to estimate the date of a target event by a combination of individual dates obtained from archaeological artifacts assumed to be contemporaneous. These dates are affected by errors of different types: laboratory and calibration curve errors, irreducible errors related to contaminations, and taphonomic disturbances, hence the possible presence of outliers. Modeling based on a hierarchical Bayesian statistical approach provides a simple way to automatically penalize outlying data without having to remove them from the dataset. Prior information on individual irreducible errors is introduced using a uniform shrinkage density with minimal assumptions about Bayesian parameters. We show that the event date model is more robust than models implemented in BCal or OxCal, although it generally yields less precise credibility intervals. The model is extended in the case of stratigraphic sequences that involve several events with temporal order constraints (relative dating), or with duration, hiatus constraints. Calculations are based on Markov chain Monte Carlo (MCMC) numerical techniques and can be performed using ChronoModel software which is freeware, open source and cross-platform. Features of the software are presented in Vibet et al. (ChronoModel v1.5 user's manual, 2016). We finally compare our prior on event dates implemented in the ChronoModel with the prior in BCal and OxCal which involves supplementary parameters defined as boundaries to phases or sequences.

Keywords

References

  1. Bayliss A (2009). Rolling out revolution: using radiocarbon dating in archaeology. Radiocarbon, 51, 123-147. https://doi.org/10.1017/S0033822200033750
  2. Bayliss A (2015). Quality in Bayesian chronological models in archaeology. World Archaeology, 47, 677-700. https://doi.org/10.1080/00438243.2015.1067640
  3. Bronk Ramsey C (1995). Radiocarbon calibration and analysis of stratigraphy: the OxCal program. Radiocarbon, 37, 425-430. https://doi.org/10.1017/S0033822200030903
  4. Bronk Ramsey C (1998). Probability and dating. Radiocarbon, 40, 461-474.
  5. Bronk Ramsey C (2001). Development of the radiocarbon calibration program OxCal. Radiocarbon, 43, 355-363. https://doi.org/10.1017/S0033822200038212
  6. Bronk Ramsey C (2008). Deposition models for chronological records. Quaternary Science Reviews, 27, 42-60. https://doi.org/10.1016/j.quascirev.2007.01.019
  7. Bronk Ramsey C (2009a). Bayesian analysis of radiocarbon dates. Radiocarbon, 51, 337-360.
  8. Bronk Ramsey C (2009b). Dealing with outliers and offsets in radiocarbon dating. Radiocarbon, 51, 1023-1045.
  9. Bronk Ramsey C, Dee M, Nakagawa T, and Staff R (2010). Developments in the calibration and modelling of radiocarbon dates. Radiocarbon, 52, 953-961.
  10. Bronk Ramsey C and Lee S (2013). Recent and planned developments of the program OxCal. Radiocarbon, 55, 720-730.
  11. Bronk Ramsey C, van der Plicht J, and Weninger B (2001). Wiggle matching radiocarbon dates. Radiocarbon, 43, 381-389. https://doi.org/10.1017/S0033822200038248
  12. Buck C, Christen J, and James G (1999). BCal: an on-line Bayesian radiocarbon calibration tool. Internet Archaeology, 7.
  13. Buck C, Kenworthy J, Litton C, and Smith A (1991). Combining archaeological and radiocarbon information: a Bayesian approach to calibration. Antiquity, 65, 808-821. https://doi.org/10.1017/S0003598X00080534
  14. Buck C, Litton C, and Shennan S (1994). A case study in combining radiocarbon and archaeological information: the early bronze age of St-Veit-Klinglberg, Land Salzburg, Austria. Germania, 72, 427-447.
  15. Buck C, Litton C, and Smith A (1992). Calibration of radiocarbon results pertaining to related archaeological events. Journal of archaeological Science, 19, 497-512.
  16. Buck CE, Higham TFG, and Lowe DJ (2003). Bayesian tools for tephrochronology. The Holocene, 13, 639-647. https://doi.org/10.1191/0959683603hl652ft
  17. Buck CE, Litton CD, and Cavanagh WG (1996). The Bayesian Approach to Interpreting Archaeological Data, Chichester, John Wiley and Sons, England.
  18. Christen J (1994). Summarizing a set of radiocarbon determinations: a robust approach. Applied Statistics, 43, 489-503. https://doi.org/10.2307/2986273
  19. Christen J and Perez S (2009). A new robust statistical model for radiocarbon data. Radiocarbon, 51, 1047-1059. https://doi.org/10.1017/S003382220003410X
  20. Combes B and Philippe A (2017). Bayesian analysis of individual and systematic multiplicative errors for estimating ages with stratigraphic constraints in optically stimulated luminescence dating. Quaternary Geochronology, 39, 24-34. https://doi.org/10.1016/j.quageo.2017.02.003
  21. Dean JS (1978). Independent dating in archaeological analysis. Advances in Archaeological Method and Theory, 1, 223-255.
  22. Desachy B (2005). Du temps ordonne au temps quantifie : application d’outils mathematiques au modele d’analyse stratigraphique d’Edward Harris. Bulletin de la Societe Prehistorique Francaise, 102, 729-740. https://doi.org/10.3406/bspf.2005.13176
  23. Desachy, B. (2008). De la formalisation du traitement des donnees stratigraphiques en archeologie de terrain. These de doctorat de l'universite de Paris 1, Paris, France.
  24. Dye T and Buck C (2015). Archaeological sequence diagrams and Bayesian chronological models. Journal of Archaeological Science, 1, 1-19. https://doi.org/10.1016/j.jasrep.2014.08.002
  25. Guerin G, Antoine P, Schmidt E, Goval EDH, Jamet G, Reyss JL, Shao Q, Philippe A, Vibet MA, and Bahain JJ (2017). Chronology of the upper Pleistocene loess sequence of Havrincourt (France) and associated Palaeolithic occupations: a Bayesian approach from Pedostratigraphy, osl, radiocarbon, tl and esr/u-series data. Quaternary Geochronology, 42, 15-30.
  26. Harris E (1989). Principles of Archaeological Stratigraphy. Interdisciplinary Statistics, XIV, 2nd edition. second ed. Academic Press, London.
  27. Lanos P and Philippe A (2017). Hierarchical Bayesian modeling for combining dates in archaeological context. Journal de la Societe Francaise de Statistique, 158, 72-88.
  28. Lanos P, Philippe A, Lanos H, and Dufresne P (2016). ChronoModel: Chronological Modelling of Archaeological Data using Bayesian Statistics. (Version 1.5) http://www.chronomodel.fr
  29. Mennessier-Jouannet C, Bucur I, Evin J, Lanos P, and Miallier D (1995). Convergence de la typologie de ceramiques et de trois methodes chronometriques pour la datation d'un four de potier a lezoux (puy-de-dome). Revue d'Archeometrie, 19, 37-47. https://doi.org/10.3406/arsci.1995.926
  30. Naylor JC and Smith AFM (1988). An archaeological inference problem. Journal of the American Statistical Association, 83, 588-595.
  31. Nicholls G and Jones M (2002). New radiocarbon calibration software. Radiocarbon, 44, 663-674. https://doi.org/10.1017/S0033822200032112
  32. Niu M, Heaton T, Blackwell P, and Buck C (2013). The Bayesian approach to radiocarbon calibration curve estimation: the intcal13, marine 13, and shcal13 methodologies. Radiocarbon, 55, 1905-1922. https://doi.org/10.2458/azu_js_rc.55.17222
  33. Pereira G, Forest M, Jadot E, and Darras V (2016). Ephemeral cities? the longevity of the postclassic tarascan urban sites of zacapu malpas and its consequences on the migration process. In Arnauld, M., Beekmann, C., and Pereira, G., editors, Ancient Mesoamerican Cities: Populations on the move, page in press. University Press of Colorado, Denver, USA.
  34. Philippe A and Vibet MA (2017a). Analysis of Archaeological Phases using the CRAN Package ArchaeoPhases, preprint hal-01347895.
  35. Philippe A and Vibet MA (2017b). ArchaeoPhases: Post-Processing of the Markov Chain Simulated by 'ChronoModel', 'Oxcal' or 'BCal'. R package version 1.3.
  36. Philippe A and Vibet MA (2017c). ArchaeoChron: Bayesian Modeling of Archaeological Chronologies. R package version 0.1.
  37. Plummer M, Best N, Cowles K, and Vines K (2006). Coda: Convergence diagnosis and output analysis for MCMC. R News, 6, 7-11.
  38. R Core Team (2017). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
  39. Vibet, MA, Philippe A, Lanos P, and Dufresne P (2016). ChronoModel v1.5 user's manual, from: www.chronomodel.fr