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Articles

Vol. 52 No. 1 (2025): CAA2025 Digital Horizons: Embracing Heritage in an Evolving World. Proceedings of the 52nd Conference on Computer Applications and Quantitative Methods in Archaeology

Seriation and Joint Probability: Unifying Archaeological Dates in the Central Mediterranean, ca. 4th-1st c. BCE

DOI
https://doi.org/10.64888/caaproceedings.v52i1.2438
Submitted
October 5, 2026
Published
2026-10-06

Abstract

Probability theory has been applied to archaeological chronology since the advent of radiocarbon dating, but key chronological indicators, such as artifact typologies, continue to be dated in descriptive terms (e.g., “in the later 3rd c. BCE”). Moreover, the informational inter-dependency for how contexts and assemblages affect others’ dating can become opaque. This paper illustrates the use of two new R packages, lakhesis and eratosthenes, to construct a wholly formal method for archaeological dating, focusing on the central Mediterranean in the last four centuries BCE. Contextual seriation is used to compare and sequence disparate contexts alongside stratigraphic relationships, to define a joint probability density function. A case study
of tombs, stratigraphic units, shipwrecks, and other depositional events is then implemented for the last four centuries BCE, illustrating how the formal estimation of events is be achieved. The resulting marginal densities can then be checked against conventional dates, not just to revise typological distinctions and revisit comparisons where discrepancies emerge, but above all to obtain a precise, probabilistic estimation of the occurrence of all archaeological events.

References

  1. Aitken, M.J. 1990. Science-based dating in archaeology. London: Longman.
  2. Baxter, M.J., and H.E.M. Cool. 2016. “Reinventing the wheel? Modelling temporal uncertainty with applications to brooch distributions in Roman Britain.” Journal of Archaeological Science 66:120–127. https://doi.org/10.1016/j.jas.2015.12.007
  3. Benoit, F. 1961. L’Épave du Grand Congloué à Marseille. Gallia Supplement 14. Paris: Centre nationale de la recherche scientifique.
  4. Benquet, L. 2013. “Lesimportations d’amphoresauIersiècle av. J.-C. : le faciès Toulousain.” In Itinéraires des vins romains en Gaule, IIIe-Ier siècles avant J.-C. Confrontation de faciès, edited by F. Olmer, 139–158. Lattes: Monographies d’Archéologie Méditerranéenne.
  5. Bernabò-Brea, L., M. Cavalier, and C.A. Livadie. 1985. “Capo Graziano, Relitto F.” In Archaeologica Subacquea 2: Isole Eolie, 88–91. Supplemento al Bolletino d’Arte 29. Rome: Istituto Poligrafico e Zecca dello Stato.
  6. Blanck, H. 1978. “Der Schiffsfund von der Secca di Capistello bei Lipari.” Mitteilungen des Deutschen Archaeologischen Instituts. Roemische Abteilung 85:91–111.
  7. Bronk Ramsey, C. 1995. “Radiocarbon Calibration and Analysis of Stratigraphy: The OxCal Program.” Radiocarbon 37:425–430. https://doi.org/10.1017/S0033822200030903.
  8. Bronk Ramsey, C. 2009. “Bayesian Analysis of Radiocarbon Dates.” Radiocarbon 51:337–360. https://doi.org/10.1017/ S0033822200033865.
  9. Bronk Ramsey, C. 2015. “Bayesian Approaches to the Building of Archaeological Chronologies.” In Mathematics and Archaeology, edited by J.A. Barcelo and I. Bogdanovich, 272–291. Boca Raton: CRC Press.
  10. Buck, C.E., W.G. Cavanagh, and C.D. Litton. 1996. Bayesian Approach to Interpreting Archaeological Data. Chichester: John Wiley & Sons. Buck, C.E., and M. Juárez. 2025. “Bayesian radiocarbon modelling for beginners.” Archaeometry 67:31–48. https://doi.org/10.1111/arcm.12998.
  11. Buck, C.E., J.B. Kenworthy, C.D. Litton, and A.F.M. Smith. 1991. “Combining archaeological and radiocarbon information: a Bayesian approach to calibration.” Antiquity 65:808–821. https://doi.org/10.1017/S0003598X00080534.
  12. Callegarin, L., M. Kbiri Alaoui, A. Ichkhakh, and J.-C. Roux, eds. 2016. Rirha : site antique et médiéval du MarocII. Période maurétanienne (Ve siècle av. J.-C.- 40 ap. J.-C.) Collection de la Casa de Velázquez 151. Madrid: Casa de Velázquez.
  13. Cavalier, M. 1985. “Il relitto A (Roghi) del Capo Graziano di Filicudi.” In Archaeologica Subacquea 2: Isole Eolie, 101–127. Supplemento al Bolletino d’Arte 29. Rome: Istituto Poligrafico e Zecca dello Stato.
  14. Cerda, D., ed. 1987a. El barco de El Sec (Costa de Calviá, Mallorca). Mallorca: Ajuntament de Calvià.
  15. Cerda, D. 1987b. “El Sec : La cerámica ática de barniz negro y las ánforas.” Revue des Études Anciennes 89:5192. Charlin, G., J.-M. Gassend, and R. Lequément. 1978. “L’épave antique de la baie de Cavalière (Le Lavandou, Var).” Archaeonautica 2:9–93.
  16. Cibecchini, F., and C. Capelli. 2013. “Nuovi dati archeologici e archeometrici sulle anfore greco-italiche: i relitti di III secolo del Mediterraneo occidentale e la possibilità di una nuova classificazione.” In Itinéraires des vins romains en Gaule, IIIe-Ier siècles avant J.-C. Confrontation de faciès, edited by F. Olmer, 423–451. Lattes: Monographies d’Archéologie Méditerranéenne.
  17. Collins-Elliott, S.A. 2026a. “eratosthenes: Synchronizing archaeological chronologies with a focus on artifact types.” Journal of Open Source Software 11 (126):9260. https://doi.org/10.21105/joss.09260.
  18. Collins-Elliott, S.A. 2026b. “Lakhesis: Consensus Seriation via Iterative Regression of Partial Rankings for Binary Data.” Journal of Applied Statistics, 1–23. https://doi.org/10.1080/02664763.2026.2672564.
  19. Cool, H.E.M., and M.J. Baxter. 1999. “Peeling the Onion: an Approach to Comparing Vessel Glass Assemblages.” Journal of Roman Archaeology 12:72–100. https://doi.org/10.1017/S1047759400017931.
  20. Corsi-Sciallano, M., and B. Liou. 1985. Les épaves de Tarraconaise à chargement d’amphores Dressel 2-4. Archaeonautica 5. Paris: Centre nationale de la recherche scientifique.
  21. Crawford, M.H. 1974. Roman Republican Coinage. Cambridge: Cambridge University Press.
  22. David, H.A., and H.N. Nagaraja. 2003. Order Statistics. 3rd ed. Hoboken, NJ: John Wiley & Sons.
  23. Dee, M., D. Wengrow, A. Shortland, A. Stevenson, F. Brock, L.G. Flink, and C. Brock Ramsey. 2013. “An absolute chronology for early Egypt using radiocarbon dating and Bayesian statistical modelling.” Proceedings of the Royal Society A 469:20130395. http://dx.doi.org/10.1098/rspa.2013.0395.
  24. Doran, J. 1971. “Computer Analysis of Data from the la Tène Cemetry at Münsingen-Rain.” In Mathematics in the Archaeological and Historical Sciences, edited by F.R. Hodson, D.G. Kendall, and P. Táutu, 422431. Edinburgh: Edinburgh University Press.
  25. Dye, T.S., and C.E. Buck. 2015. “Archaeological sequence diagrams and Bayesian chronological models.” Journal of Archaeological Science 63:84–93. https://doi.org/10.1016/j.jas.2015.08.008.
  26. Fernández-Miranda, M., M. Belén, D. Cerdá, and J. de Nicolas. 1977. Arqueología submarina en Menorca. Madrid: Fundacion Juan Merch.
  27. Flegal, J.M., M. Haran, and G.L. Jones. 2008. “Markov Chain Monte Carlo: Can We Trust the Third Significant Figure?” Statistical Science 23:250–260. https://doi.org/10.1214/08-STS257.
  28. Frey, D., F.D. Hentschel, and D.H. Keith. 1978. “Deepwater archaeology. The Capistello wreck excavation, Lipari, Aeolian Islands.” International Journal of Nautical Archaeology 7:279–300. https://doi.org/10. 1111/j.1095-9270.1978.tb01079.x.
  29. Geman, S., and D. Geman. 1984. “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images.” IEEE Transactions on Pattern Analysis and Machine Intelligence 6:721–741.
  30. Hahsler, M., K. Hornik, and C. Buchta. 2008. “Getting Things in Order: An Introduction to the R Package seriation.” Journal of Statistical Software 25:1–34. https://doi.org/10.18637/jss.v025.i03.
  31. Haslett, J., and A.C. Parnell. 2008. “A Simple Monotone Process with Application to Radiocarbon-Dated Depth Chronologies.” Journal of the Royal Statistical Society: Series C (Applied Statistics) 57:399–418. https://doi.org/10.1111/j.1467-9876.2008.00623.x.
  32. Hesnard, A., M.-B. Carre, M. Rival, and B. Dangréaux. 1988. L’épave romaine Grand Ribaud D (Hyères, Var). Paris: Centre nationale de la recherche scientifique.
  33. Hyndman, R.J. 1996. “Computing and Graphing Highest Density Regions.” The American Statistician 50:120–126. https://doi.org/10.2307/2684423.
  34. Ihm, P. 2005. “AContribution to the History of Seriation in Archaeology.” In Classification– The Ubiquitous Challenge, edited by C. Weihs and W. Gaul, 307–316. Berlin: Springer.
  35. Jehasse, J., and L. Jehasse. 1973. La nécropole préromaine d’Aléria (1960-1968). Paris: Centre nationale de la recherche scientifique. . 2001. Aléria. Nouvelles données de la nécropole. Lyon: Maison de l’Orient et de la Méditerranée Jean Pouilloux.
  36. Johnson, N.L., S. Kotz, and N. Balakrishnan. 1995. Continuous Univariate Distributions, Volume 2. 2nd ed. NewYork: John Wiley & Sons.
  37. Jones, G.L., M. Haran, B.S. Caffo, and R. Neath. 2006. “Fixed-Width Output Analysis for Markov Chain Monte Carlo.” Journal of the American Statistical Association 101:1537–1547. https://doi.org/10.1198/ 016214506000000492.
  38. Lamboglia, N. 1952. “Per una classificazione preliminare della ceramica campana.” In Atti del I Congresso Internazionale di Studi Liguri, Monaco, Bordighera, Genova, 10-17 aprile, 1950, 193–206. Bordighera.
  39. Lamboglia, N. 1964. “La campagna 1963 sul relitto di Punta Scaletta all’Isola di Giannutri.” Rivista di Studi Liguri 30:219–228.
  40. Lancel, S., J.-P. Morel, and J.-P. Thuillier. 1982. Byrsa II: rapports préliminaires sur les fouilles 1977-1978 : niveaux et vestiges puniques. Collection de l’École française de Rome. Rome: École française de Rome.
  41. Lee, S., and C. Bronk Ramsey. 2012. “Development and Application of the Trapezoidal Model for Archaeological Chronologies.” https://doi.org/10.2458/azu_js_rc.v54i1.12397. Radiocarbon 54:107–122.
  42. Levy, E. 2025. “Temporal relations in archaeology: a survey and a new typology.” Archaeometry 67 (S1): 178199. https://doi.org/10.1111/arcm.13080.
  43. Liou, B., and P. Pomey. 1985. “Recherches archéologiques sous-marines.” Gallia 43:547–576. Long, L. 1987. “Les épaves du Grand Congloué. Étude du journal de fouille de Fernand Benoit.” Archaeonautica 7:9–36. https://doi.org/10.3406/nauti.1987.896.
  44. Loughton, M.E. 2014. The Arverni and Roman Wine: Roman Amphorae from Late Iron Age Sites in the Auvergne (Central France): Chronology, Fabrics and Stamps. Archaeopress Roman Archaeology 2. Oxford: Archaeopress.
  45. Manning, S.W., B. Lorentzen, and S. Demesticha. 2022. “Dating Mediterranean shipwrecks: the Mazotos ship, radiocarbon dating and the need for independent chronological anchors.” Antiquity 96:968–980. https://doi.org/10.15184/aqy.2022.76.
  46. Maurer, W., and B.H. Margolin. 1976. “The Multivariate Inclusion-Exclusion Formula and Order Statistics from Dependent Variates.” Annals of Statistics 46:1190–1199. https://doi.org/10.1214/aos/1176343650.
  47. Mazard, J. 1955. Corpus Nummorus Numidiae Mauretaniaeque. Paris: Arts et Métiers Graphiques.
  48. McCormick, W.T., S.F. Deutsch, J.J. Martin, and P.J. Schweitzer. 1969. Identification of Data Structures and Relationships by Matrix Reordering Techniques. P-512. Arlington, VA: Institute for Defense Analyses.
  49. Miró,J. 1991. “Unconjuntodeánforastardo-republicanasdeunsilodelpobladoibéricodeBurriac(Cabrera de Mar, Barcelona).” Saguntum 24:53–68.
  50. Morel, J.-P. 1981. Céramique campanienne: les formes. BEFAR 244. Rome: École Française de Rome.
  51. Nicholls, G., and M. Jones. 2002. “Radiocarbon Dating with Temporal Order Constraints.” Journal of the Royal Statistical Society Series C: Applied Statistics 50:503–521. https://doi.org/10.1111/1467-9876. 00250.
  52. Noukpoape, K.M., P. Lanos, and P. Dufresne. 2025. “A new conservative and robust Bayesian approach for the event date model in chronology building.” Archaeometry 67 (S1): 84–109. https://doi.org/10.1111/ arcm.13063.
  53. O’Brien, M.J., and R.L.Lyman.1999. Seriation, Stratigraphy, and Index Fossils: The Backbone of Archaeological Dating. New York: Springer.
  54. Olcese, G. 2004. “Anfore greco-italiche antiche: alcune osservazioni sull’origine e sulla circolazione alla luce di recenti ricerche archeologiche ed archeometriche.” In Metodi e approcci archeologici: l’industria e il commercio nell’Italia antica, edited by E.C. De Sena and H. Dessales, 173–192. BAR International Series 1262. Oxford: Archaeopress.
  55. Olcese, G. 2005. “The Production and Circulation of Greco-Italic Amphorae of Campania (Ischia/Bay of Naples). The data of the archaeological and archaeometric research.” Skyllis: Zeitschrift für Unterwasserarchäologie 7:60–75.
  56. Orlandini, P. 1956. “Deposito di anfore ellenistiche in Via Polieno [Gela].” Notizie degli Scavi 10:355–357.
  57. Parker, A.J. 1992. Ancient Shipwrecks of the Mediterranean and the Roman Provinces. BAR International Series 580. Oxford: British Archaeological Reports.
  58. Poblome, J., and J.F. Groenen. 2003. “Constrained Correspondence Analysis for Seriation of Sagalassos Tablewares.” In The Digital Heritage of Archaeology: Computer Applications and Quantitative Methods in Archaeology, edited by M. Doerr and A. Sarris, 301–306. Athens: Hellenic Ministry of Culture.
  59. Py, M., ed. 1993. Dicocer: Dictionnaire des céramiques antiques (VIIe s. av. n. è.-VIIe s. de n. è.) en Méditerranée nord-occidentale (Provence, Languedoc, Ampurdan). Lattara 6. Lattes: Association pour la Recherche Archéologique en Languedoc Oriental. https://www.syslat.fr/SLC/DICOCER/d.index.html.
  60. Py, M., ed. 2004. Le quartier 30-35 de la ville de Lattara (fin IIIe- Ier s. av. n. è.). Regards sur la vie urbaine à la fin de la Protohistoire. Lattara 17. Lattes: Edition de l’Association pour la Recherche Archéologique en Languedoc Oriental.
  61. Py, M., A.M. Adroher Auroux, and C. Sanchez, eds. 2001. Dicocer 2: Corpus des céramiques de l’Âge du Fer de Lattes (fouilles 1963-1999). Lattara 14. Lattes: Association pour la Recherche Archéologique en Languedoc Oriental. https://www.syslat.fr/SLC/DICOCER/d.index.html.
  62. R Core Team. 2024. R: A Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing. http://www.r-project.org/.
  63. Reimer, P.J., W.E.N. Austin, E. Bard, A. Bayliss, P.G. Blackwell, C. Bronk Ramsey, M. Butzin, et al. 2020. “TheIntCal20NorthernHemisphereRadiocarbonAgeCalibrationCurve(0–55calkBP).”Radiocarbon 62:725–757. https://doi.org/10.1017/RDC.2020.41.
  64. Smith, A.F.M., and G.O. Roberts. 1993. “Bayesian Computation Via the Gibbs Sampler and Related Markov Chain Monte Carlo Methods.” Journal of the Royal Statistical Society. Series B (Methodological) 55:3–23. https://doi.org/10.1111/j.2517-6161.1993.tb01466.x.
  65. Steier, P., and W. Rom. 2000. “The Use of Bayesian Statistics for 14C Dates of Chronologically Ordered Samples: A Critical Analysis.” Radiocarbon 42:183–198. https://doi.org/10.1017/S0033822200058999.
  66. Taylor, R.E., and Ofer Bar-Yosef. 2014. Radiocarbon Dating: An Archaeological Perspective. 2nded. NewYork: Routledge. https://doi.org/10.4324/9781315421216.
  67. Tchernia, A. 1978. L’Épave romaine de la Madrague de Giens (Var), campagnes 1972-1975. Paris: Centre nationale de la recherche scientifique.
  68. Tchernia, A. 1986. Le vin de l’Italie romaine. Essai d’histoire économique d’après les amphores. Rome: École Française de Rome.
  69. Van Dorp, J.R., and S. Kotz. 2003. “Generalized trapezoidal distributions.” Metrika 58:85–97. https://doi. org/10.1007/s001840200230.
  70. Van de Velden, M., P.J.F. Groenen, and J. Poblome. 2009. “Seriation by Constrained Correspondence Analysis: A Simulation Study.” Computational Statistics & Data Analysis 53:3129–3138. https://doi.org/10.1016/j.csda.2008.08.020.
  71. Vandermersch, C. 1994. Vins et amphores de Grande Grèce et de Sicile, IVe-IIIe s. avant J.-C. Naples: Centre Jean Bérard.