Concepts of probability in radiocarbon analysis

Documenta Praehistorica

Volumn 38, Issue 1, 2011, Pages 1-20

  Weninger, Bernhard ^a   Edinborough, Kevan ^b   Clare, Lee ^b   Jöris, Olaf ^c  

^a UNIVERSITY OF COLOGNE   (Germany)

^b UNIVERSITY COLLEGE LONDON   (United Kingdom)

^c Forschungsbereich Altsteinzeit   (Germany)

Author keywords

Bayesian inference; Chronology; Noncommutative algebra; Noncommutative probability; Radiocarbon calibration

Indexed keywords

EID: 84861783431     PISSN: 1408967X     EISSN: 18542492     Source Type: Journal    
DOI: 10.4312/dp.38.2     Document Type: Review

References (65)

1. BAYES T. R. 1763. An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society 53: 370-418.
2. BAYLISS A. 2009. Rolling Out Revolution; Using Radiocarbon Dating in Archaeology. Radiocarbon 51(1): 123-147.
3. BLAAUW M., BAKKER R., CHRISTEN J. A., HALL V. A. and VAN DER PLICHT J. 2007. A Bayesian Framework for age modelling of Radiocarbon-dated peat deposits: Case studies from the Netherlands. Radiocarbon 49(2): 357-367.
4. BLOCKLEY S. E., HOUSLEY R. A. 2009. Calibration Commentary. Radiocarbon 51(1): 287-290.
5. BREUNIG P. 1987. 14C-Chronologie des vorderasiatischen, südost- u. mitteleuropäischen Neolithikums. Fundamenta Reihe A, 13. Köln/Wien.
6. BRONK RAMSEY C., VAN DER PLICHT J. and WENINGER B. 2001. 'Wiggle matching' radiocarbon dates. Radiocarbon 43(2A): 381-389.
7. BRONK RAMSEY C. 1994. Analysis of chronological information and radiocarbon calibration: the program OxCal. Archaeological Computing Newsletter 41: 11-6.
8. 1995. Radiocarbon calibration and analysis of stratigraphy: the OxCal program. Radiocarbon 37(2): 425-430.
9. 2009. Bayesian Analysis of Radiocarbon Dates. Radiocarbon 51(1): 337-360.
10. BUCHANAN B., HAMILTON M., EDINBOROUGH K., O'BRIEN M. J. and COLLARD M. A. 2011. Comment on Steele's (2010) "Radiocarbon dates as data: quantitative strategies for estimating colonization front speeds and event densities". Journal of Archaeological Science 38(9): 2116-2122, doi: 10.1016/j.jas.2011.02. 026
11. BUCK C. E. 2011. BCal, an on-line radiocarbon calibration tool: http://bcal.shef.ac.uk
12. BUCK C. E., CAVANAGH W. G., LITTON C. D. 1996. Bayesian approach to Interpreting Archaeological Data. Wiley. Chichester.
13. BUCK C. E., CHRISTEN J. A. and JAMES G. N. 1999. BCal: an on-line Bayesian radiocarbon calibration tool. Internet Archaeology 7. online http://intarch.ac.uk/journal/issue13/christen-index.html
14. CHRISTEN J. A. 1993. Bwigg: an internet facility for Bayesian Radiocarbon Wiggle Matching. Internet Archaeology 13. online http://intarch.ac.uk/journal/ issue13/christen-index.html
15. CHRISTEN J. A., LITTON C. D. 1995. A Bayesian approach to wiggle-matching. Journal of Archaeological Science 22(6): 719-725.
16. COLLARD M., EDINBOROUGH K., SHENNAN S. and THOMAS M. G. 2010. Radiocarbon Evidence indicates that migrants introduced farming to Britain. Journal of Archaeological Science 37: 866-870.
17. CONARD N. J., BOLUS M. 2003. Radiocarbon dating the appearance of modern humans and timing of cultural innovations in Europe: new results and new challenges. Journal of Human Evolution 44: 331-371.
18. CULLETON B. J. 2008. Crude demographic proxy reveals nothing about Paleoindian population. Proceedings of the National Academy of Sciences of the United States of America 105 (50): E111.
19. DANZEGLOCKE U., WENINGER B. and JÖRIS O. 2007. Online Radiocarbon Age Calibration: www.calpal-online.de.online http://download.calpal.de/calpal- download/
20. DEHLING H., VAN DER PLICHT J. 1993. Statistical Problems in Calibrating Radiocarbon Dates. Radiocarbon 35 (1): 239-244.
21. DIRAC P. A. M 1947. The Principles of Quantum Mechanics. 3rd edition. Oxford University Press. Oxford.
22. DE JONG A. F. M., MOOK W. G. and BECKER B. 1979. Confirmation of the Suess wiggles: 3200-3700 BC. Nature 280: 48-49.
23. EADIE W. D., DRYARD D., JAMES F. E., ROOS M. and SADOULET B. 1971. Statistical Methods in Experimental Physics. North Holland Publishing Co. Amsterdam: 17-23.
24. EINSTEIN A., PODOLSKY B. and ROSEN N. 1935. Can quantum-mechanical description of physical reality be considered complete? Physical Review 47: 777-780, doi:10.1103/PhysRev.47.777.
25. FAIRBANKS R. G., MORTLOCK R. A., CHIU T.-C., CAO L., KAPLAN A., GUILDERSON T. P., FAIRBANKS T. W., BLOOM A. L., GROOTES P. M. and NADEAU M.-J. 2005. Radiocarbon calibration curve spanning 10,000 to 50,000 years BP based on paired 230Th/234U/238U and 14C dates on pristine corals. Quaternary Science Reviews 25: 1781-1796.
26. GEYH M. 1969. Versuch einer chronologischen Gliederung des marinen Holozän an der Nordseeküste mit Hilfe der statistischen Auswertung von 14C-Daten. Zeitschrift der Deutschen Geologischen Gesellschaft 188(2): 351-360.
27. 1971. Middle and young Holocene sea-level changes as global contemporary events. Geologiska Föreningens i Stockholm Förhandlingar 93: 679-692.
28. 1980. Holocene sea-level history: Case study of the statistical evaluation of 14C dates. In M. Stuiver and R. S. Kra (eds.), Proceedings of the 10th Internationa114C Conference. Radiocarbon 22(3): 695-704.
29. GKIASTA M., RUSSELL T., SHENNAN S. and STEELE J. 2003. Neolithic Transition in Europe: the radiocarbon record revisited. Antiquity 77(295): 45-62.
30. JAGUTTIS-EMDEN M. 1977. Zur Präzision archäologischer Datierungen. Archaeologica Venatoria 4. Tübingen.
31. JONES M., NICHOLLS G. K. 2003. New radiocarbon calibration software. Radiocarbon 44(3): 663-674.
32. KOLMOGOROV A. 1933. Grundbegriffe der Wahrscheinlichkeitsrechnung. Ergebnisse der Mathematik. 2. Band, Heft 3, Berlin. online http://www. mathematik.com/Kolmogorov/index.html
33. KOLMOGOROV A. N. 1956. Foundations of the Theory of Probability. New York. Chelsea Publishing Company.
34. MICHCZYNSKA D. J., PAZDUR M. F. and WALANUS A. 1990. Bayesian approach to probabilistic calibration of radiocarbon ages. In W. G. Mook and H. T. Waterbolk (eds.), Proceedings of the 2nd International Symposium 14C and Archaeology. PACT 29. Strasbourg: 69-79.
35. NIKLAUS T. R. 1993. Beschleunigermassenspektrometrie von Radioisotopen. Unpublished doctoral dissertation University of Zürich. Zürich. ETH Nr. 10065, doi:10.3929/ethz-a-000697402
36. OTTAWAY J. H., OTTAWAY B. 1975. Irregularities in the Dendrochronological Calibration Curve. In T. Watkins (ed.), Radiocarbon, Calibration and Prehistory. Edinburgh University Press, Edinburgh: 28-38.
37. PARNELL A. C., HASLETT J., ALLEN J. R. M., BUCK C. E. and HUNTLEY B. 2008. A flexible approach to assessing synchroneity of past events using Bayesian reconstructions of sedimentation history. Quaternary Science Reviews 27: 1872-1885.
38. PAZDUR M. F., MICHCZYNSKA D. J. 1989. Improvement of the procedure for probabilistic calibration of radiocarbon. Radiocarbon 31(3): 824-832.
39. PEARSON G. W. 1986. Precise calendrical dating of known growth-period samples using a 'curve fitting' technique. Radiocarbon 28: 292-299.
40. 1987. How to cope with calibration. Antiquity 61(231): 98-103.
41. POPPER K. R. 1934. Logik der Forschung. Julius Springer. Wien.
42. RÉDEI M. 1992. When can non-commutative statistical inference be Bayesian? International Studies in the Philosophy of Science 6: 129-132. http://phil.elte.hu/~redei/cikkek/bayesi.pdf
43. REIMER P. J., REIMER R. 2011. CALIB. Online http://calib.qub.ac.uk/calib/
44. REIMER P. J., BAILLIE M. G. L., BARD E., BAYLISS A., BECK J. W., BERTRAND C. J. H., BLACKWELL P. G., BUCK C. E., BURR G. S., CUTLER K. B., DAMON P. E., EDWARDS R. L., FAIRBANKS R. G., FRIEDRICH M., GUILDERSON T. P., HOGG A. G., HUGHEN K. A., KROMER B., MCCORMAC F. G., MANNING S. W., RAMSEY C. B., REIMER R. W., REMMELE S., SOUTHON J. R., STUIVER M., TALAMO S., TAYLOR F. W., VAN DER PLICHT J. and WEYHENMEYER C. E. 2004. IntCal04 terrestrial radiocarbon age calibration, 26-0 ka BP. Radiocarbon 46: 1029-1058.
45. REIMER P. J., BAILLIE M. G. L., BARD E. BAYLISS A., BECK J. W., BLACKWELL P. G., BRONK RAMSEY C., BUCK C. E., BURR G. S., EDWARDS R. L., FRIEDRICH M., GROOTES P. M., GUILDERSON T. P., HAJDAS I., HEATON T. J., HOGG A. G., HUGHEN K. A., KAISER K. F., KROMER B., MCCORMAC F. G., MANNING S. W., REIMER R. W., RICHARDS A. A., SOUTHON J. R., TALAMO S., TURNEY C. S. M., VAN DER PLICHT J. and WEYHENMEYER C. E. 2009. IntCal09 and Marine09 radiocarbon age calibration curves, 0-50,000 years cal BP. Radiocarbon 51: 1111-1150.
46. 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.
47. STEELE J. 2010 Radiocarbon dates as data: quantitative strategies for estimating colonization front speeds and event densities. Journal of Archaeological Science 37: 2017-2030.
48. STOLK A. D., HOGERVORST K. and BERENDSEN H. 1989. Correcting 14C Histograms for the Non-Linearity of the Radiocarbon Time Scale. Radiocarbon 31(2): 169-178.
49. STOLK A. D., TÖRNQUIST T. E., KILIAN P., BERENDSEN H. J. A. and VAN DER PLICHT J. 1994. Calibration of 14C Histograms: A Comparison of Methods. Radiocarbon 36(1): 1-10.
50. STUIVER M., KRA R. 1986. Radiocarbon Calibration Issue. Proceedings of the 12th International Radiocarbon Conference, June 24-28, Trondheim, Norway. In M. Stuiver and R. Kra (eds.), Radiocarbon 28(2B): 805-1030.
51. STUIVER M., REIMER P. J. 1989. Histograms obtained from computerized radiocarbon age calibration. Radiocarbon 31(3): 817-823.
52. 1993. Extended 14C data base and revised CALIB 3.0 14C age calibration program. Radiocarbon 35(1): 215-230.
53. STUIVER M., REIMER P. J. and REIMER R. W. 2005. CALIB5.0. online http://calib.qub.ac.uk/calib/
54. SUESS H. E., 1970. Bristlecone pine calibration of the radiocarbon time-scale 5200 BC to the present. In I. U. Olsson (ed.), Radiocarbon variations and absolute chronology. Proceedings of Nobel symposium, 12th. John Wiley & Sons, New York: 303-311.
55. SZÉKELY G. J. 1990. Paradoxa. Klassische und neue Überraschungen aus Wahrscheinlichkeitstheorie und mathematischer Statistik. Verlag Harri Deutsch. Thun und Frankfurt am Main.
56. TAKESAKI M. 1972. Conditional Expectations in von Neumann Algebras. Journal of Functional Analysis 9: 306.
57. VALENTE G. 2007. Is there a stability problem for Bayesian noncommutative probabilities? Studies in History and Philosophy of Modern Physics 38: 832-843.
58. VAN ANDEL T. H. 2005. The ownership of time: approved 14C calibration or freedom of choice? Antiquity 79: 944-948.
59. VAN DER PLICHT T. H. 1993. The Groningen Radiocarbon Calibration Program. Radiocarbon 35(1): 231-237.
60. 2011. WinCal25. online http://www.rug.nl/ees/informatieVoor/cioKlanten? lang=en
61. WENINGER B. 1986. High-precision calibration of archaeological radiocarbon dates. Acta Interdisciplinaria Archaeol 4: 11-53.
62. 1997. Studien zur dendrochronologischen Kalibration von archäologischen 14C-Daten. Habelt Verlag. Frankfurt/M.
63. WENINGER B., JÖRIS O. 2008. A 14C age calibration curve for the last 60 ka: the Greenland-Hulu U/Th timescale and its impact on understanding the Middle to Upper Paleolithic transition in Western Eurasia. Journal of Human Evolution 55: 772-781.
64. WENINGER B., CLARE L., ROHLING E., BAR-YOSEF O., BOHNER U., BUDJA M., BUNDSCHUH M., FEURDEAN A., GEBEL H-G, JORIS O., LINSTADTER J., MAYEWSKI P., MUHLENBRUCH T., REINGRUBER A., ROLLEFSON G., SCHYLE D., THISSEN L., TODOROVA H. and ZIELHOFER C. 2009. The Impact of Rapid Climate Change on prehistoric societies during the Holocene in the Eastern Mediterranean. In M. Budja (ed.), 16th Neolithic Studies. Documenta Praehistorica 36: 7-59.
65. WENINGER F., STEIER P., KUTSCHERA W. and WILD E. M. 2010. Robust Bayesian Analysis, an attempt to improve Bayesian Sequencing. Radiocarbon 52(2-3): 962-983.