Dealing with outliers and offsets in radiocarbon dating
Open accessAbstract
The wide availability of precise radiocarbon dates has allowed researchers in a number of disciplines to address chronological questions at a resolution which was not possible 10 or 20 years ago. The use of Bayesian statistics for the analysis of groups of dates is becoming a common way to integrate all of the 14 C evidence together. However, the models most often used make a number of assumptions that may not always be appropriate. In particular, there is an assumption that all of the 14 C measurements are correct in their context and that the original 14 C concentration of the sample is properly represented by the calibration curve. In practice, in any analysis of dates some are usually rejected as obvious outliers. However, there are Bayesian statistical methods which can be used to perform this rejection in a more objective way (Christen 1994b), but these are not often used. This paper discusses the underlying statistics and application of these methods, and extensions of them, as they are implemented in OxCal v 4.1. New methods are presented for the treatment of outliers, where the problems lie principally with the context rather than the 14 C measurement. There is also a full treatment of outlier analysis for samples that are all of the same age, which takes account of the uncertainty in the calibration curve. All of these Bayesian approaches can be used either for outlier detection and rejection or in a model averaging approach where dates most likely to be outliers are downweighted. Another important subject is the consistent treatment of correlated uncertainties between a set of measurements and the calibration curve. This has already been discussed by Jones and Nicholls (2001) in the case of marine reservoir offsets. In this paper, the use of a similar approach for other kinds of correlated offset (such as overall measurement bias or regional offsets in the calibration curve) is discussed and the implementation of these methods in OxCal v 4.0 is presented.
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The RScaled outlier model in OxCal was employed because errors involved in this study are of the 14C timescale and may be understated, making RScaled more appropriate than SSimple.
“The RScaled outlier model in OxCal was employed as the errors involved in this study are of the 14C timescale (and not the tree-ring/calendar timescale), but may reasonably be regarded as potentially somewhat understated in real terms, as evident, for example, in previous high-precision inter-laboratory comparisons [64]–thus the RScaled option seems more appropriate/realistic in a case like ours”
From Integrated Tree-Ring-Radiocarbon High-Resolution Timeframe to Resolve Earlier Second Millennium BCE Mesopotamian Chronology (2016) · cites this paper as [63]
In the Outlier_Model section (page unavailable), the paper identifies RScaled as an option for offsets in the ¹⁴C ratio whose scale is unknown, rather than offsets in calendar time. But it distinguishes those offsets from understated measurement uncertainties: its Introduction and Outlier_Model section treat measurement errors as s-type, represented by SSimple. The paper therefore supports the timescale distinction, but not the stated reason for preferring RScaled over SSimple; it does not establish the citing study’s inter-laboratory premise. (LLM, conf=0.86)
Experimental — accuracy not yet measuredThe OxCal General Outlier model is applied to dates on short or shorter-lived samples and combinations of such dates to detect and down-weight outliers proportionally.
“The OxCal General Outlier model is applied to dates on short or shorter-lived samples (including some instances of wood-charcoal dates where it is evident any in-built age factor must be consistently very minor to negligible: see below) and for combinations of such dates (unless in a tree-ring sequenced wiggle-match) to detect and then down-weight outliers proportionally [138].”
From Second Intermediate Period date for the Thera (Santorini) eruption and historical implications (2022) · cites this paper as [138]
The Outlier_Model section recommends the General model for most purposes, and Additional information describes using posterior outlier probabilities to average over accepting and rejecting dates. The paper does not specify short-lived samples or combinations of their dates as the General model’s particular applications; its combination-of-dates example uses a different outlier model. (LLM, conf=0.83)
Experimental — accuracy not yet measuredDates within an R_Combine or Combine function, or dates forming part of a tree-ring defined wiggle-match, were assessed and down-weighted as outliers using the OxCal SSimple Outlier model.
“Dates within an R_Combine (or Combine) function, or dates forming part of a tree-ring defined wiggle-match [139, 140], were assessed and down-weighted as outliers using the OxCal SSimple Outlier model [138].”
From Second Intermediate Period date for the Thera (Santorini) eruption and historical implications (2022) · cites this paper as [138]
The ‘Outliers with Underestimated Uncertainties (s-type)’ section defines OxCal’s SSimple model for radiocarbon dates, and the ‘Combination of Dates for Samples of the Same Age’ example applies outlier analysis within R_Combine. The paper does not establish its use for dates in a tree-ring-defined wiggle-match; that part of the citing sentence is accompanied by separate citations [139, 140]. The indexed passages provide no page numbers. (LLM, conf=0.82)
Experimental — accuracy not yet measuredOutlier probabilities were defined for each sample based on its carbon mass.
“Outlier probabilities (44) were defined for each sample based on its carbon mass ( SI Appendix , Table S1 and Figs. S3 and S5).”
From A high-precision chronological model for the decorated Upper Paleolithic cave of Chauvet-Pont d’Arc, Ardèche, France (2016) · cites this paper as [44]
OxCal 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 [63]
An OxCal ΔR test indicates a bimodal finding for the MBA time series versus the calibration curve.
“An OxCal ΔR test24, to assess whether there is systematic difference between the MBA time series and the calibration curve using a neutral prior (0 ± 10 14C years), indicates in many cases a bimodal finding (Supplementary Fig. S1).”
From Radiocarbon offsets and old world chronology as relevant to Mesopotamia, Egypt, Anatolia and Thera (Santorini) (2020) · cites this paper as [24]
The wiggle-match calendar placement of the Hd GOR time series uses the placement with satisfactory OxCal agreement indices after removing the 13 or 14 largest outliers; this places the last year of the chronology RY1,764, with bark (felling date) ~748BCE.
“The wiggle-match calendar placement of the Hd GOR time series22 uses the placement with satisfactory OxCal agreement indices after removing the 13 or 14 largest outliers (SSimple outlier model24 applied to individual dates, dates in weighted averages, and the weighted averages42). The minimum almost satisfactory case removes 13 individual outliers and achieves Amodel ~ 58 and Aoverall ~ 61, while”
From Radiocarbon offsets and old world chronology as relevant to Mesopotamia, Egypt, Anatolia and Thera (Santorini) (2020) · cites this paper as [24]
Dates on wood-charcoal where some in-built age cases are likely are employed with the OxCal Charcoal Outlier model applied to approximately reduce the likely in-built age element.
“Dates on wood-charcoal where some in-built age cases are likely are employed with the OxCal Charcoal Outlier model applied to approximately reduce the likely in-built age element [138].”
From Second Intermediate Period date for the Thera (Santorini) eruption and historical implications (2022) · cites this paper as [138]
The OxCal SSimple outlier model is used to test for and down-weight outliers within the wiggle-match.
“The OxCal SSimple outlier model is used to test for and to down-weight outliers within the wiggle-match [138].”
From Second Intermediate Period date for the Thera (Santorini) eruption and historical implications (2022) · cites this paper as [138]
The use of Bayesian models to identify outlier dates is well developed in the OxCal open source software and discussed extensively by Bronk Ramsay.
“Second, the use of Bayesian models to identify outlier dates is well developed in the OxCal open source software and discussed extensively by Bronk Ramsay [27].”
From Bayesian Modeling and Chronological Precision for Polynesian Settlement of Tonga (2015) · cites this paper as [27]
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“Whelan [95, p. 70, 73] noted that the same name Teti-mesu also occurs on figures [184] in the tomb complex TT15 of Tetiky, who was the mayor of Thebes during the reign of Nebpehtire Ahmose and apparently died during the reign of Amenhotep I [183–188].”
Influential
- Authors
- Bronk Ramsey, C.
- Venue
- Radiocarbon
- Publisher
- Cambridge University Press (CUP)
- Published
- 2009
- Volume
- 51
- Issue
- 3
- Pages
- 1023-1045
- ISSN
- 0033-8222 (ISSN-L)
- 1945-5755
- OpenAlex
- W68289770
- Cited by
- 1,204
- References
- 20
- Citations by year
- 2026: 56 · 2025: 71 · 2024: 84 · 2023: 112 · 2022: 93 · 2021: 130 · 2020: 95 · 2019: 97 · 2018: 74 · 2017: 84 · 2016: 58 · 2015: 54 · 2014: 54 · 2013: 59 · 2012: 43
- FWCI
- 21.24
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Radiocarbon (publishedVersion)
- UA Campus Repository (The University of Arizona) (acceptedVersion)
- Funders
- Leverhulme Trust
- 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, outlier detection, outlier removal, Bayesian analysis, OxCal, measurement bias, model averaging, correlated uncertainties, chronological analysis
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