Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T05:08:12.320Z Has data issue: false hasContentIssue false
  • English
  • Français

Combining archaeological and radiocarbon information: a Bayesian approach to calibration

Published online by Cambridge University Press:  02 January 2015

C. E. Buck ,
J. B. Kenworthy ,
C. D. Litton  and
A. F. M. Smith
C. E. Buck
Affiliation:
Department of Mathematics, University of Nottingham, Nottingham NG7 2RD
J. B. Kenworthy
Affiliation:
Department of Archaeology, University of Nottingham, Nottingham NG7 2RD
C. D. Litton
Affiliation:
Department of Mathematics, University of Nottingham, Nottingham NG7 2RD
A. F. M. Smith
Affiliation:
Department of Mathematics, Imperial College, London SW7 2BZ
Get access Rights & Permissions [Opens in a new window]

Extract

A recent and significant improvement in radiocarbon dating has been the increased ability of the radiocarbon laboratories to provide results combining precision with accuracy. This improvement has been accompanied by increasing recognition that the information must be expressed on the calendar, rather than on the radiocarbon, time-scale. Despite the attempts of Ottaway (1987) and Pearson (1987), archaeologists are not sufficiently aware of the statistical problems involved in the transformation from one scale to the other: ‘Some of the trouble lies in the ignorance of radiocarbon consumers; the many attempts to educate them can have only limited success when radiocarbon study depends on statistical concepts and methods far beyond the average archaeologist’s innumerate grasp’ (Chippindale 1990: 203).

Type
Research Article
Information
Antiquity , Volume 65 , Issue 249 , December 1991 , pp. 808 - 821
Copyright
Copyright © Antiquity Publications Ltd 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The essential question of how to convert radiocarbon determinations - those physical figures so beguilingly expressed in ‘radiocarbon years before present’which are not years at all - remains open to debate. In this new contribution, an approach is outlined using Bayesian methods, rather than classical statistics.

References

Aitchison, T.C. et al. 1989. A comparison of methods used for the calibration of radiocarbon dates, Radiocarbon 31(3): 846–62.Google Scholar
Barnett, V. 1982. Comparative statistical inference. 2nd edition. New York (NY): Wiley.Google Scholar
Bayes, T.R. 1763. An essay towards solving a problem in the doctrine of chances, Philosophical Transactions of the Royal Society 53: 370–418.Google Scholar
Bowman, S. 1990. Interpreting the past: radiocarbon dating. London: British Museum Publications.Google Scholar
Bowman, S. & Balaam, N. 1990. Using radiocarbon, Antiquity 64: 315–18.Google Scholar
Box, G.E.P. & Tiao, G.C. 1973. Bayesian inference in statistical analysis. Reading (MA): Addison-Wesley.Google Scholar
Buck, C.E., Cavanagh, W.G. & Litton, CD. 1988. The spatial analysis of site phosphate data, in Rahtz, S.P.Q. (ed.), Computer applications and quantitative methods in archaeology, 1988: 151–60. Oxford: British Archaeological Reports. International series 446(i).Google Scholar
Buck, C.E. & Litton, C.D. 1989. Image segmentation for archaeological geochemical data, in Rahtz, S.P.Q. (ed.), Computer applications and quantitative methods in archaeology, 1989: 133–44. Oxford: British Archaeological Reports. International series 548.Google Scholar
Buck, C.E. & Litton, C.D. 1991. A computational Bayes approach to some common archaeological problems, in Lockyear, & Rahtz, (ed.): 93–9.Google Scholar
Cavanagh, W.G., Hirst, S. & Litton, C.D. 1988. Soil phosphate, site boundaries and change-point analysis, Journal of Field Archaeology 15(1): 67–83.Google Scholar
Chippindale, C. 1990. Editorial, Antiquity 64: 203–9.CrossRefGoogle Scholar
Clarke, D.V. 1976a. Excavations at Skara Brae: a summary account, in Burgess, C.B. & Miket, R. (ed.), Settlement and economy in the third and second millennia BC: 233’50. Oxford: British Archaeological Reports. British series 33.Google Scholar
Clarke, D.V. 1976b. The Neolithic village at Skara Brae, Orkney: 1972–73 excavations, an interim report. Edinburgh: HMSO.Google Scholar
DeGroot, M.H. 1970. Optimal statistical decisions. New York (NY): McGraw-Hill.Google Scholar
Doran, J.E. & Hodson, F.R. (ed.). 1975. Mathematics and computers in archaeology. Edinburgh: Edinburgh University Press.Google Scholar
De Finetti, B. 1974–5. Theory of probability: a critical introductory treatment. New York (NY): Wiley.Google Scholar
Freeman, P.R. 1976. A Bayesian approach to the megalithic yard, Journal of the Royal Statistical Society A 139: 20–55.Google Scholar
Helskog, K. & Schweder, T. 1989. Estimating the number of contemporaneous houses from 14C dates, Antiquity 63: 166–72.Google Scholar
Jeffreys, H.S. 1961. Theory of probability. 3rd edition. Oxford: Oxford University Press.Google Scholar
Kadane, J.B. & Hastorf, C.A. 1986. Accurate approximations for posterior moments and marginal densities, Journal of the American Statistical Association 81: 82–8.Google Scholar
Lee, P.M. 1989. Bayesian statistics: an introduction. Oxford: Oxford University Press.Google Scholar
Lindley, D.V. 1965. Introduction to probability and statistics from a Bayesian viewpoint. Cambridge: Cambridge University Press.Google Scholar
Lindley, D.V. 1985. Making decisions. 2nd edition. London: Wiley.Google Scholar
Lindley, D.V. 1990. The 1988 Wald memorial lectures: the present position in Bayesian statistics, Statistical Science 5(1): 44–89.Google Scholar
Litton, C.D. & Leese, M.N. 1991. Some statistical problems arising in radiocarbon calibration, in Lockyear, & Rahtz, (ed.): 101–9.Google Scholar
Lockyear, K. & Rahtz, S.P.Q. (ed.). 1991. Computer applications and quantitative methods in archaeology, 1990. Oxford: British Archaeological Reports. International series 565.Google Scholar
Naylor, J.C. & Smith, A.F.M. 1988. An archaeological inference problem, Journal of the American Statistical Association 83(403): 588–95.Google Scholar
O’Hagan, A. 1988. Probability: methods and measurements. London: Chapman & Hall.Google Scholar
Orton, C. 1980. Mathematics in archaeology. Glasgow: William Collins.Google Scholar
Orton, C. 1983. A statistical technique for integrating 14C dates with other forms of dating evidence, in Haigh, J.G.B. (ed.), Computer applications and quantitative methods in archaeology. 1983: 115–24. Bradford: University of Bradford, School of Archaeological Sciences.Google Scholar
Ottaway, B.S. 1987. Radiocarbon: where we are and where we need to be, Antiquity 61: 135–7.CrossRefGoogle Scholar
Pearson, G.W. 1987. How to cope with calibration. Antiquity 61: 98–103.Google Scholar
Pearson, G.W., Pilcher, J.R., Baillie, M.G.L., Corbett, D.M. & Qua, F. 1986. High-precision 14C measurements of Irish oaks to show the natural 14C variations from AD 1840–5210 BC, Radiocarbon 28(2B): 911–34.Google Scholar
Pearson, G.W. & Stuiver, M. 1986. High-precision calibration of the radiocarbon time scale, 500–2500 BC, Radiocarbon 28(2B): 839–62.Google Scholar
Phillips, L.D. 1973. Bayesian statistics for social scientists. London: Nelson.Google Scholar
Richards, C. 1990. Postscript: the Late Neolithic settlement complex at Barnhouse Farm, Stenness, in Renfrew, C. (ed.), The prehistory of Orkney, 4000 BC-1000 AD: 305–16. 2nd edition. Edinburgh: Edinburgh University Press.Google Scholar
Scott, E.M., Baxter, M.S. & Aitchison, T.C. 1984. A comparison of the treatment of errors in radiocarbon dating calibration methods, Journal of Archaeological Science 11(6): 455–66.Google Scholar
Scott, E.M., Baxter, M.S., Harkness, D.D., Aitchison, T.C. & Cook, G.T. 1988. The comparability of results across a sub-section of radiocarbon laboratories, in Slater, E.A. & Tate, J.O. (ed.), Science and archaeology 1987: 581–89. Oxford: British Archaeological Reports. British series 196(i).Google Scholar
Smith, J.Q. Decision analysis: a Bayesian approach. London: Chapman & Hall.Google Scholar
Stuiver, M. & Pearson, G.W. 1986. High-precision calibration of the radiocarbon time scale, AD 1950–500 BC, Radiocarbon 28(2B): 805–38.Google Scholar
Stuiver, M. & Reimer, P. A computer program for radiocarbon age calibration, Radiocarbon 28(2B): 1022–30.Google Scholar
Vincent, CH. 1988. Treatment of discrepancies in radiocarbon dating, Radiocarbon 30: 2157–60.CrossRefGoogle Scholar
Ward, G.K. & Wilson, S.R. 1978. Procedures for comparing and combining radiocarbon age determinations: a critique, Archaeometry 20: 19–31.Google Scholar