Bayesian Analysis of Radiocarbon Dates
Open accessAbstract
If radiocarbon measurements are to be used at all for chronological purposes, we have to use statistical methods for calibration. The most widely used method of calibration can be seen as a simple application of Bayesian statistics, which uses both the information from the new measurement and information from the 14 C calibration curve. In most dating applications, however, we have larger numbers of 14 C measurements and we wish to relate those to events in the past. Bayesian statistics provides a coherent framework in which such analysis can be performed and is becoming a core element in many 14 C dating projects. This article gives an overview of the main model components used in chronological analysis, their mathematical formulation, and examples of how such analyses can be performed using the latest version of the OxCal software (v4). Many such models can be put together, in a modular fashion, from simple elements, with defined constraints and groupings. In other cases, the commonly used “uniform phase” models might not be appropriate, and ramped, exponential, or normal distributions of events might be more useful. When considering analyses of these kinds, it is useful to be able run simulations on synthetic data. Methods for performing such tests are discussed here along with other methods of diagnosing possible problems with statistical models of this kind.
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Agreement between the posterior and prior distributions follows the OxCal v4.1 convention in which 60% is the threshold for acceptance for individual and overall agreement indices.
“The agreement between the posterior distribution of the data and the prior distribution follows the convention of OxCal ν 4.1 where 60% is taken as the threshold for acceptance for individual and overall agreement indices”
From Chronology of the Early Bronze Age in the Southern Levant: New Analysis for a High Chronology (2012) · cites this paper as Bronk Ramsey 2009
In “Inconsistencies Between Measurements and the Model,” the paper describes an individual agreement index with a reasonable minimum acceptable value around 60%, and says overall indices falling much below 60% warrant investigation. It does not present 60% as a firm acceptance threshold: it explicitly says the agreement-index approach has no well-defined cut-off. The comparison is between posterior distributions under the full model and a null prior, rather than simply between a posterior and a prior distribution. (LLM, conf=0.85)
Experimental — accuracy not yet measuredThe OxCal modelling of the destruction and specific use event Phases as exponentially distributed towards the end of the Phase, with the destruction/event as the Boundary immediately following, likely accurately describes the data, including not over-estimating the age because of a few older/residual samples.
“The OxCal modelling of the destruction and specific use event Phases as exponentially distributed towards the end of the Phase, with the destruction/event as the Boundary immediately following, thus likely accurately describes the data, including, but not over-estimating the age because of a few samples that are older, residual, or include more substantial in-built age (e.g.wood charcoal that is”
From Second Intermediate Period date for the Thera (Santorini) eruption and historical implications (2022) · cites this paper as [57]
Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredLarge datasets covering long, continuous stratigraphic sequences are best able to contribute to chronological debates, since prior knowledge of relative order can be used to constrain radiocarbon probabilities using Bayesian statistics.
“Large datasets covering long, continuous stratigraphic sequences are best able to contribute to chronological debates, since prior knowledge of relative order can be used to constrain the radiocarbon probabilities using Bayesian statistics [116–118].”
From The chronology of Gezer from the end of the late bronze age to iron age II: A meeting point for radiocarbon, archaeology egyptology and the Bible (2023) · cites this paper as [118]
The Relative Constraints section explains that stratigraphic order can be incorporated as a prior in Bayesian chronological models. The Multiple Phases section calls analyses with well-defined stratigraphic constraints especially robust and powerful, but it does not say that datasets must be large or cover long, continuous sequences to contribute most to chronological debates. (LLM, conf=0.86)
Experimental — accuracy not yet measuredUsing OxCal with IntCal20 and no adjustments for geographical location, the Kenyon samples yield calibrated dates ranging from 1699-1623 calBC (70.3% probability, GrN-18368) to 1617-1531 calBC (95.4% probability, GrN-18539), with the outlier GrN-18538 at 2031-1899 calBC (95.4% probability).
“Using OxCal with IntCal20 and no adjustments for geographical location, these samples would yield calibrated dates ranging from 1699 to 1623 calBC 70.3% probability (GrN-18368) to 1617-1531 calBC 95.4% probability (GrN-18539), with the outlier (GrN-18538) 2031-1899 calBC 95.4% probability”
From The Bronze Age Destruction of Jericho, Archaeology, and the Book of Joshua (2023) · cites this paper as Bronk Ramsey 2009, pp.337-60
Split into 2 atoms — 0 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 1 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredOxCal implements a comprehensive Bayesian chronological modelling approach that permits definition of probability regions and robust outlier detection.
“the OxCal software implements a comprehensive Bayesian chronological modelling approach [62]; among other things, this permits definition of probability regions and robust outlier detection [62, 63].”
From Integrated Tree-Ring-Radiocarbon High-Resolution Timeframe to Resolve Earlier Second Millennium BCE Mesopotamian Chronology (2016) · cites this paper as [62]
The calibrated 14C date of mudbrick lump sample GrM-15201 (3385 ± 20 BP) using OxCal and IntCal20 has 68.3% probability ranges 1729-1725 (4.1%) and 1689-1628 (64.2%) cal BCE, and 95.4% ranges 1741-1710 (20.4%) and 1698-1619 (75.0%) cal BCE.
“Using the OxCal program [72,90] with the IntCal20 calibration curve [59], the 68.3% probability calibrated age ranges (Fig 7) are 1729–1725 (4.1%), 1689–1628 (64.2%) cal BCE, while the broader 95.4% probability ranges are 1741–1710 (20.4%), 1698–1619 (75.0%) cal BCE.”
From The Minoan Thera eruption predates Pharaoh Ahmose: Radiocarbon dating of Egyptian 17th to early 18th Dynasty museum objects (2025) · cites this paper as [72]
Calibrating GrA-64347 using OxCal and IntCal20 gives an age range 1542-1427 cal BCE (66.4%) with highest probability.
“Using OxCal [72,90] with IntCal20 [59], the age range 1542–1427 cal BCE (66.4%) has the highest probability, visually shown by the tallest peaks of the calibrated age graph (Fig 8).”
From The Minoan Thera eruption predates Pharaoh Ahmose: Radiocarbon dating of Egyptian 17th to early 18th Dynasty museum objects (2025) · cites this paper as [72]
Calibrating DRI-2948 using OxCal with IntCal20 yields a 95.4% probability date of 1881-1626 cal BCE.
“We calibrated this result, using OxCal [72,90] with the latest calibration curve IntCal20 [59], yielding a 95.4% probability date of 1881–1626 cal BCE.”
From The Minoan Thera eruption predates Pharaoh Ahmose: Radiocarbon dating of Egyptian 17th to early 18th Dynasty museum objects (2025) · cites this paper as [72]
Bayesian statistical approaches can enhance the precision of chronometric estimates and can make outputs more robust and reliable.
“This technique can enhance the precision of chronometric estimates (Bronk Ramsey 2009) and can make outputs more robust and reliable (Dee and Bronk Ramsey 2014;Lee and Bronk Ramsey 2012).”
From The Egyptian Predynastic and State Formation (2016) · cites this paper as Bronk Ramsey 2009
The calibrated radiocarbon dates for the 15 individuals broadly range between 1670 and 1950 ce.
“The results were calibrated to take into account marine reservoir effects derived from the consumption of marine proteins, and broadly range between 1670 and 1950 ce28–30 (Supplementary Information section 2).”
From Ancient Rapanui genomes reveal resilience and pre-European contact with the Americas (2024) · cites this paper as [29]
The Probability Density Functions section explains radiocarbon calibration methods, but does not report dates for 15 individuals. A search for the 1670–1950 CE range and marine reservoir effects found no passage in our copy addressing those results. (LLM, conf=0.76)
Experimental — accuracy not yet measured
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“and OxCal [43, 61, 62] expressed in terms of RY776 following the previous chronology based on the Gordion RY sequence and dates published [21–23,”
MethodInfluentialSelf-citationThe impact of Bayesian chronologies on the British Iron Age
Hamilton, W. D., Haselgrove, C., & Gosden, C. (2015) · World Archaeology · doi:10.1080/00438243.2015.1053976 · Cited by 62 · see citing works
Social responses to climate change in Iron Age north-east Thailand: new archaeobotanical evidence
Castillo, C. C., Higham, C. F. W., Miller, K., Chang, N., Douka, K., Higham, T. F. G., & Fuller, D. Q. (2018) · Antiquity · doi:10.15184/aqy.2018.198 · Cited by 61 · see citing works
Kutschera, W., Bietak, M., Wild, E. M., Ramsey, C. B., Dee, M., Golser, R., Kopetzky, K., Stadler, P., Steier, P., Thanheiser, U., et al. (2012) · Radiocarbon · doi:10.1017/s0033822200047172 · Cited by 58 · see citing works
Self-citationRadiocarbon re-dating of contact-era Iroquoian history in northeastern North America
Manning, S. W., Birch, J., Conger, M. A., Dee, M. W., Griggs, C., Hadden, C. S., Hogg, A. G., Ramsey, C. B., Sanft, S., Steier, P., et al. (2018) · Science Advances · doi:10.1126/sciadv.aav0280 · Cited by 54 · see citing works
Self-citationManning, S. W., Griggs, C., Lorentzen, B., Bronk Ramsey, C., Chivall, D., Jull, A. J. T., & Lange, T. E. (2018) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1719420115 · Cited by 51 · see citing works
Soil organic carbon and nitrogen accumulation rates in cold and alpine environments over 1Ma
Egli, M., Favilli, F., Krebs, R., Pichler, B., & Dahms, D. (2012) · Geoderma · doi:10.1016/j.geoderma.2012.03.017 · Cited by 47 · see citing works
Höflmayer, F., Kamlah, J., Sader, H., Dee, M. W., Kutschera, W., Wild, E. M., & Riehl, S. (2016) · Bulletin of the American Schools of Oriental Research · doi:10.5615/bullamerschoorie.375.0053 · Cited by 42 · see citing works
IntCal20 Tree Rings: An Archaeological Swot Analysis
Bayliss, A., Marshall, P., Dee, M. W., Friedrich, M., Heaton, T. J., & Wacker, L. (2020) · Radiocarbon · doi:10.1017/rdc.2020.77 · Cited by 40 · see citing works
Sharp, W. D., Kahn, J. G., Polito, C. M., & Kirch, P. V. (2010) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1005063107 · Cited by 39 · see citing works
The Date of the Minoan Santorini Eruption: Quantifying the “Offset”
Höflmayer, F. (2012) · Radiocarbon · doi:10.1017/s0033822200047196 · Cited by 39 · see citing works
Kirch, P. V., Molle, G., Nickelsen, C., Mills, P., Dotte‐Sarout, E., Swift, J., Wolfe, A., & Horrocks, M. (2015) · Archaeology in Oceania · doi:10.1002/arco.5050 · Cited by 35 · see citing works
Best, J., Doherty, S., Armit, I., Boev, Z., Büster, L., Cunliffe, B., Foster, A., Frimet, B., Hamilton-Dyer, S., Higham, T., et al. (2022) · Antiquity · doi:10.15184/aqy.2021.90 · Cited by 35 · see citing works
Manning, S. W., Wacker, L., Büntgen, U., Bronk Ramsey, C., Dee, M. W., Kromer, B., Lorentzen, B., & Tegel, W. (2020) · Scientific Reports · doi:10.1038/s41598-020-69287-2 · Cited by 35 · see citing works
Mediterranean radiocarbon offsets and calendar dates for prehistory
Manning, S. W., Kromer, B., Cremaschi, M., Dee, M. W., Friedrich, R., Griggs, C., & Hadden, C. S. (2020) · Science Advances · doi:10.1126/sciadv.aaz1096 · Cited by 41 · see citing works
McAneney, J., & Baillie, M. (2019) · Antiquity · doi:10.15184/aqy.2018.165 · Cited by 33 · see citing works
Hudson, A. M., Quade, J., Ali, G., Boyle, D., Bassett, S., Huntington, K. W., De los Santos, M. G., Cohen, A. S., Lin, K., & Wang, X. (2017) · Geochimica et Cosmochimica Acta · doi:10.1016/j.gca.2017.06.024 · Cited by 32 · see citing works
Asscher, Y., Cabanes, D., Hitchcock, L. A., Maeir, A. M., Weiner, S., & Boaretto, E. (2015) · Radiocarbon · doi:10.2458/azu_rc.57.18391 · Cited by 31 · see citing works
Storozum, M., Liu, H., Qin, Z., Ming, K., Fu, K., Wang, H., & Kidder, T. (2018) · Geoarchaeology · doi:10.1002/gea.21634 · Cited by 30 · see citing works
The Hakaea Beach site, Marquesan colonisation, and models of East Polynesian settlement
ALLEN, M. S., & McALISTER, A. J. (2010) · Archaeology in Oceania · doi:10.1002/j.1834-4453.2010.tb00080.x · Cited by 30 · see citing works
Manning, S. W., & Kromer, B. (2012) · Radiocarbon · doi:10.1017/s0033822200047202 · Cited by 29 · see citing works
Regev, J., Finkelstein, I., Adams, M. J., & Boaretto, E. (2015) · Ägypten und Levante · doi:10.1553/s241 · Cited by 28 · see citing works
Allen, M. S., & Morrison, A. E. (2013) · Journal of Archaeological Science · doi:10.1016/j.jas.2013.06.008 · Cited by 26 · see citing works
Chronogeographic Variation in Initial East Polynesian Construction of Monumental Ceremonial Sites
Martinsson-Wallin, H., Wallin, P., Anderson, A., & Solsvik, R. (2013) · The Journal of Island and Coastal Archaeology · doi:10.1080/15564894.2013.834009 · Cited by 25 · see citing works
Kusumoto, S., Goto, T., Sugai, T., Omori, T., & Satake, K. (2018) · Marine Geology · doi:10.1016/j.margeo.2018.07.004 · Cited by 24 · see citing works
Quiles, A., Aubourg, E., Berthier, B., Delque-Količ, E., Pierrat-Bonnefois, G., Dee, M. W., Andreu-Lanoë, G., Bronk Ramsey, C., & Moreau, C. (2013) · Journal of Archaeological Science · doi:10.1016/j.jas.2012.05.026 · Cited by 24 · see citing works
Self-citationNew integrated molecular approaches for investigating lake settlements in north-western Europe
Brown, A. G., Fonville, T., van Hardenbroek, M., Cavers, G., Crone, A., McCormick, F., Murray, E., Mackay, H., Whitehouse, N. J., Henderson, A. C. G., et al. (2022) · Antiquity · doi:10.15184/aqy.2022.70 · Cited by 21 · see citing works
Evolution and Legacy of East Asian Aurochs
Hou, J., Guan, X., Xia, X., Lyu, Y., Liu, X., Mazei, Y., Xie, P., Chang, F., Zhang, X., Chen, J., et al. (2024) · Science Bulletin · doi:10.1016/j.scib.2024.09.016 · Cited by 22 · see citing works
A New Annual<sup>14</sup>C Dataset for Calibrating the Thera Eruption
Friedrich, R., Kromer, B., Wacker, L., Olsen, J., Remmele, S., Lindauer, S., Land, A., & Pearson, C. (2020) · Radiocarbon · doi:10.1017/rdc.2020.33 · Cited by 20 · see citing works
Radiocarbon dating the Late Bronze Age: Cultural and Historical Considerations on Megiddo and Beyond
Martin, M. A. S., Finkelstein, I., & Piasetzky, E. (2020) · Bulletin of the American Schools of Oriental Research · doi:10.1086/709576 · Cited by 20 · see citing works
Second Radiocarbon Intercomparison Program for the Chauvetpont d'Arc Cave, Ardèche, France
Quiles, A., Valladas, H., Geneste, J.-M., Clottes, J., Baffler, D., Berthier, B., Brock, F., Ramsey, C. B., Delqué-Količ, E., Dumoulin, J.-P., et al. (2014) · Radiocarbon · doi:10.2458/56.16940 · Cited by 20 · see citing works
Population genomics of the muskox' resilience in the near absence of genetic variation
Pečnerová, P., Lord, E., Garcia‐Erill, G., Hanghøj, K., Rasmussen, M. S., Meisner, J., Liu, X., van der Valk, T., Santander, C. G., Quinn, L., et al. (2024) · Molecular Ecology · doi:10.1111/mec.17205 · Cited by 19 · see citing works
Webster, L. C., Wolff, S. R., Ortiz, S. M., Barbosa, M., Coyle, C., Arbino, G. P., Dee, M. W., Hua, Q., & Jacobsen, G. E. (2023) · PLOS ONE · doi:10.1371/journal.pone.0293119 · Cited by 20 · see citing works
Ehrlich, Y., Regev, L., & Boaretto, E. (2018) · Scientific Reports · doi:10.1038/s41598-018-29392-9 · Cited by 19 · see citing works
Ancient Rapanui genomes reveal resilience and pre-European contact with the Americas
Moreno-Mayar, J. V., Sousa da Mota, B., Higham, T., Klemm, S., Gorman Edmunds, M., Stenderup, J., Iraeta-Orbegozo, M., Laborde, V., Heyer, E., Torres Hochstetter, F., et al. (2024) · Nature · doi:10.1038/s41586-024-07881-4 · Cited by 20 · see citing works
“29 and Supplementary Table 22) and characterized by five main parameters.”
A history of the LBK in the central Polish lowlands
Whittle, A., Marciniak, A., Pyzel, J., Krueger, M., Lisowski, M., Ramsey, C. B., Dunbar, E., Barclay, A., Bayliss, A., & Gaydarska, B. (2022) · Praehistorische Zeitschrift · doi:10.1515/pz-2022-2041 · Cited by 15 · see citing works
Regev, J., Gadot, Y., Uziel, J., Chalaf, O., Shalev, Y., Roth, H., Shalom, N., Szanton, N., Bocher, E., Pearson, C. L., et al. (2024) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2321024121 · Cited by 17 · see citing works
Radiocarbon dating and the Naqada relative chronology
Dee, M. W., Wengrow, D., Shortland, A. J., Stevenson, A., Brock, F., & Bronk Ramsey, C. (2014) · Journal of Archaeological Science · doi:10.1016/j.jas.2014.03.016 · Cited by 16 · see citing works
The complex history of Pueblo Bonito and its interpretation
Crown, P. L., & Wills, W. H. (2018) · Antiquity · doi:10.15184/aqy.2018.138 · Cited by 16 · see citing works
Second Intermediate Period date for the Thera (Santorini) eruption and historical implications
Manning, S. W. (2022) · PLOS ONE · doi:10.1371/journal.pone.0274835 · Cited by 13 · see citing works
Olive shrub buried on Therasia supports a mid-16th century BCE date for the Thera eruption
Pearson, C., Sbonias, K., Tzachili, I., & Heaton, T. J. (2023) · Scientific Reports · doi:10.1038/s41598-023-33696-w · Cited by 13 · see citing works
Manning, S. W. (2024) · Radiocarbon · doi:10.1017/rdc.2024.44 · Cited by 9 · see citing works
“…some probability spread across the plateau portion, these offer situations where properly constructed Bayesian Chronological Modeling (e.g. Bronk Ramsey 2009a; Bayliss 2009) integrating the prior knowledge (the known sequence) with the radiocarbon dating probability can serve to varying…”
BackgroundBioarchaeology of human skeletons from an elite tomb at Pacopampa in Peru’s northern highlands.
NAGAOKA, T., SEKI, Y., HIDALGO, J. P. V., & CHOCANO, D. M. (2020) · Anthropological Science · doi:10.1537/ase.200218 · Cited by 7 · see citing works
New evidence for Middle Bronze Age chronology from the Syro-Anatolian frontier
Herrmann, V. R., Manning, S. W., Morgan, K. R., Soldi, S., & Schloen, D. (2023) · Antiquity · doi:10.15184/aqy.2023.30 · Cited by 7 · see citing works
Scales of plant stewardship in the precontact Pacific Northwest, USA
Carney, M., & Connolly, T. (2024) · The Holocene · doi:10.1177/09596836241247307 · Cited by 4 · see citing works
“All 28 radiocarbon dates were recalibrated using OxCal 4.4.1 with the IntCal 20 curve (Bronk Ramsey, 2009; Reimer et al., 2020).”
InfluentialIn search of Estonia’s earliest chicken
Ehrlich, F., Rannamäe, E., Laneman, M., Tõrv, M., Lang, V., Oras, E., & Lõugas, L. (2021) · Estonian Journal of Archaeology · doi:10.3176/arch.2021.2.04 · Cited by 3 · see citing works
Resolution of the High versus Low debate for Old and Middle Kingdom Egypt
Erdil, P., Webster, L., Kuitems, M., Knoblauch, C., Bestock, L., Höflmayer, F., Beeckman, H., Fuller, D. Q., Manning, S. W., & Dee, M. W. (2025) · PLOS One · doi:10.1371/journal.pone.0314612 · Cited by 3 · see citing works
The Bronze Age Destruction of Jericho, Archaeology, and the Book of Joshua
Kennedy, T. (2023) · Religions · doi:10.3390/rel14060796 · Cited by 3 · see citing works
Mieth, A., Kühlem, A., Vogt, B., & Bork, H.-R. (2022) · Developments in Paleoenvironmental Research · doi:10.1007/978-3-030-91127-0_19 · Cited by 2 · see citing works
Czerniak, L., Bayliss, A., Goslar, T., Badura, M., Budilová, K., Lisá, L., Marciniak, A., Matuszewska, A., Pędziszewska, A., & Święty-Musznicka, J. (2024) · Journal of Field Archaeology · doi:10.1080/00934690.2024.2306433 · Cited by 2 · see citing works
Bruins, H. J., & van der Plicht, J. (2025) · PLOS One · doi:10.1371/journal.pone.0330702 · Cited by 1 · see citing works
“This issue has been treated statistically in detail by Bronk Ramsey in the development of the OxCal program [72,90].”
InfluentialCzerniak, L. (2025) · Journal of Archaeological Method and Theory · doi:10.1007/s10816-024-09669-2
“Bayesian chronological modeling was conducted using OxCal 4.4 (Bronk Ramsey 2009) and the internationally agreed calibration curve for the Northern Hemisphere (IntCal20; Reimer et al. 2020).”
Influential
- Authors
- Bronk Ramsey, C.
- Venue
- Radiocarbon
- Publisher
- Cambridge University Press (CUP)
- Published
- 2009
- Volume
- 51
- Issue
- 1
- Pages
- 337-360
- ISSN
- 0033-8222 (ISSN-L)
- 1945-5755
- OpenAlex
- W2167452694
- Cited by
- 8,725
- References
- 46
- Citations by year
- 2026: 549 · 2025: 606 · 2024: 663 · 2023: 724 · 2022: 680 · 2021: 757 · 2020: 651 · 2019: 589 · 2018: 556 · 2017: 607 · 2016: 434 · 2015: 441 · 2014: 438 · 2013: 412 · 2012: 273
- FWCI
- 158.23
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Radiocarbon (publishedVersion)
- UA Campus Repository (The University of Arizona) (acceptedVersion)
- Funders
- Natural Environment Research Council (NE/E019129/1)
- Topics
- Physical Sciences › Earth and Planetary Sciences › Paleontology › Archaeology and ancient environmental studies
- Physical Sciences › Earth and Planetary Sciences › Atmospheric Science › Geology and Paleoclimatology Research
- Physical Sciences › Earth and Planetary Sciences › Atmospheric Science › Tree-ring climate responses
- Keywords
- radiocarbon dating, Bayesian calibration, OxCal, chronological analysis, synthetic data simulation, model diagnostics, radiocarbon chronology
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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