MatCalib: a Matlab software package for Bayesian modeling of radiocarbon ages subject to temporal order constraints

Shiyong Yu; Shiyong Yu

doi:10.3934/geosci.2022002

AIMS Geosciences

2022, Volume 8, Issue 1: 16-32. doi: 10.3934/geosci.2022002

Previous Article Next Article

Research article Special Issues

MatCalib: a Matlab software package for Bayesian modeling of radiocarbon ages subject to temporal order constraints

Shiyong Yu ^,

School of Geography, Geomatics, and Planning, Jiangsu Normal University, 101 Shanghai Road, Xuzhou, Jiangsu 221116, China

Received: 11 September 2021 Revised: 10 December 2021 Accepted: 20 December 2021 Published: 06 January 2022

Radiocarbon ages must be calibrated due to the remarkable fluctuations of the atmospheric radiocarbon level. The traditional method (e.g., Calib) does not make use of any constraint such as the temporal/stratigraphical ordering of the ages, thereby resulting in one or several large age ranges. Bayesian age modeling is advantageous over the traditional method in several aspects. First, it can provide precise age estimates by applying some constraints known a priori. Second, it may provide a timing of an archaeological feature or a geological event that is unable to be dated directly. Although several Bayesian age modeling frameworks have been developed, inexperienced users may need not only a more user-friendly environment for data entry and definition of their project-specific problem, but also a powerful post-processing tool for analyzing and visualizing the results. Here a hierarchical Bayesian model with a minimum level of structural complexity is presented. It provides users with a flexible and powerful framework to incorporate radiocarbon ages into a sequence along a one-dimensional continuum so that it best reveals their temporal order, thereby yielding a more precise timing. The accompanying Matlab software package not only complements the existing MatCal package designed to calibrate radiocarbon ages individually, but also serves as an alternative to the online tools of Bayesian radiocarbon age modeling such as OxCal and BCal.
- radiocarbon dating,
- calibration curve,
- Bayesian age modeling,
- temporal order,
- MatCalib,
- Period, Sequence
Citation: Shiyong Yu. MatCalib: a Matlab software package for Bayesian modeling of radiocarbon ages subject to temporal order constraints[J]. AIMS Geosciences, 2022, 8(1): 16-32. doi: 10.3934/geosci.2022002

Related Papers:

Abstract

Radiocarbon ages must be calibrated due to the remarkable fluctuations of the atmospheric radiocarbon level. The traditional method (e.g., Calib) does not make use of any constraint such as the temporal/stratigraphical ordering of the ages, thereby resulting in one or several large age ranges. Bayesian age modeling is advantageous over the traditional method in several aspects. First, it can provide precise age estimates by applying some constraints known a priori. Second, it may provide a timing of an archaeological feature or a geological event that is unable to be dated directly. Although several Bayesian age modeling frameworks have been developed, inexperienced users may need not only a more user-friendly environment for data entry and definition of their project-specific problem, but also a powerful post-processing tool for analyzing and visualizing the results. Here a hierarchical Bayesian model with a minimum level of structural complexity is presented. It provides users with a flexible and powerful framework to incorporate radiocarbon ages into a sequence along a one-dimensional continuum so that it best reveals their temporal order, thereby yielding a more precise timing. The accompanying Matlab software package not only complements the existing MatCal package designed to calibrate radiocarbon ages individually, but also serves as an alternative to the online tools of Bayesian radiocarbon age modeling such as OxCal and BCal.

References

[1]	Bronk Ramsey C (2008) Radiocarbon dating: revolutions in understanding. Archaeometry 50: 249-275. https://doi.org/10.1111/j.1475-4754.2008.00394.x doi: 10.1111/j.1475-4754.2008.00394.x
[2]	Libby WF (1961) Radiocarbon dating. Science 133: 621-629.
[3]	Heaton T, Bard E, Bronk Ramsey C, et al. (2021) Radiocarbon: A key tracer for studying Earth's dynamo, climate system, carbon cycle, and Sun. Science 374: eabd7096. https://doi.org/10.1126/science.abd7096 doi: 10.1126/science.abd7096
[4]	Siegenthaler U, Heimann M, Oeschger H (1980) ¹⁴C variations caused by changes in the global carbon cycle. Radiocarbon 22: 177-191. https://doi.org/10.1017/S0033822200009449 doi: 10.1017/S0033822200009449
[5]	Guilderson TP, Reimer PJ, Brown TA (2005) The boon and bane of radiocarbon dating. Science 307: 362-364. https://doi.org/10.1126/science.1104164 doi: 10.1126/science.1104164
[6]	Clark RM (1975) A calibration curve for radiocarbon dates. Antiquity 49: 251-266. https://doi.org/10.1017/S0003598X00070277 doi: 10.1017/S0003598X00070277
[7]	Bronk Ramsey C (1995) Radiocarbon calibration and analysis of stratigraphy: the OxCal program. Radiocarbon 37: 425-430. https://doi.org/10.1017/S0033822200030903 doi: 10.1017/S0033822200030903
[8]	Buck CE, Kenworthy JB, Litton CD, et al. (1991) Combining archaeological and radiocarbon information: a Bayesian approach to calibration. Antiquity 65: 808-821. https://doi.org/10.1017/S0003598X00080534 doi: 10.1017/S0003598X00080534
[9]	Yu SY, Chen X, Fang Z, et al. (2021) Towards a precise timing of groundwater use in the lower Yellow River area during the late Bronze Age: Bayesian inference from the radiocarbon ages of ancient water wells at the Liang'ercun site, North China. Quat Geochronol 66: 101214. https://doi.org/10.1016/j.quageo.2021.101214 doi: 10.1016/j.quageo.2021.101214
[10]	Gómez-Paccard M, Rivero-Montero M, Chauvin A, et al. (2019) Revisiting the chronology of the Early Iron Age in the north-eastern Iberian Peninsula. Archaeol Anthropol Sci 11: 4755-4767. https://doi.org/10.1007/s12520-019-00812-9 doi: 10.1007/s12520-019-00812-9
[11]	Bronk Ramsey C (2001) Development of the radiocarbon program OxCal. Radiocarbon 43: 355-363.
[12]	Buck CE, Meson B (2015) On being a good Bayesian. World Archaeol 47: 567-584. https://doi.org/10.1080/00438243.2015.1053977 doi: 10.1080/00438243.2015.1053977
[13]	Heaton TJ, Blackwell PG, Buck CE (2009) A Bayesian approach to the estimation of radiocarbon calibration curves: the IntCal09 methodology. Radiocarbon 51: 1151-1164. https://doi.org/10.1017/S0033822200034214 doi: 10.1017/S0033822200034214
[14]	Nicholls G, Jones M (2001) Radiocarbon dating with temporal order constraints. J R Stat Soc 50: 503-521. https://doi.org/10.1111/1467-9876.00250 doi: 10.1111/1467-9876.00250
[15]	Guntau M (1989) Concepts of natural law and time in the history of geology. Earth Sci Hist 8: 106-110. https://doi.org/10.17704/eshi.8.2.02w88w234323x503 doi: 10.17704/eshi.8.2.02w88w234323x503
[16]	Harris EC (1979) The laws of archaeological stratigraphy. World Archaeol 11: 111-117.
[17]	Jones M, Nicholls G (2002) New radiocarbon calibration software. Radiocarbon 44: 663-674. https://doi.org/10.1017/S0033822200032112 doi: 10.1017/S0033822200032112
[18]	Buck CE, Christen JA, James GN (1999) BCal: an on-line Bayesian radiocarbon calibration tool. Internet Archaeol 7: 1192-1201. https://doi.org/10.11141/ia.7.1 doi: 10.11141/ia.7.1
[19]	Yu SY (2021) Bayesian radiocarbon age modeling. Mendeley Data, V1. https://doi.org/10.17632/sfdwkyh848.1
[20]	Reimer P, Baillie M, Bard E, et al. (2004) IntCal04 terrestrial radiocarbon age calibration, 0-26 cal kyr BP. Radiocarbon 46: 1029-1058. https://doi.org/10.1017/S0033822200032999 doi: 10.1017/S0033822200032999
[21]	Bronk Ramsey C (2009) Bayesian analysis of radiocarbon dates. Radiocarbon 51: 337-360. https://doi.org/10.1017/S0033822200033865 doi: 10.1017/S0033822200033865
[22]	Christen JA, Pérez ES (2009) A new robust statistical model for radiocarbon data. Radiocarbon 51: 1047-1059. https://doi.org/10.1017/S003382220003410X doi: 10.1017/S003382220003410X
[23]	Gilks WR, Best NG, Tan KK (1995) Adaptive rejection Metropolis sampling within Gibbs sampling. J R Stat Soc 44: 455-472. https://doi.org/10.2307/2986138 doi: 10.2307/2986138
[24]	Chib S, Greenberg E (1995) Understanding the Metropolis-Hastings algorithm. Am Stat 49: 327-335. https://doi.org/10.2307/2684568 doi: 10.2307/2684568
[25]	Reimer PJ, Austin WE, Bard E, et al. (2020) The IntCal20 Northern Hemisphere radiocarbon age calibration curve (0-55 cal kBP). Radiocarbon 62: 725-757. https://doi.org/10.1017/RDC.2020.41 doi: 10.1017/RDC.2020.41
[26]	Hogg AG, Heaton TJ, Hua Q, et al. (2020) SHCal20 Southern Hemisphere calibration, 0-55,000 years cal BP. Radiocarbon 62: 759-778. https://doi.org/10.1017/RDC.2020.59 doi: 10.1017/RDC.2020.59
[27]	Heaton TJ, Köhler P, Butzin M, et al. (2020) Marine20—the marine radiocarbon age calibration curve (0-55,000 cal BP). Radiocarbon 62: 779-820. https://doi.org/10.1017/RDC.2020.68 doi: 10.1017/RDC.2020.68
[28]	Gelman A, Inference and monitoring convergence, In: Gilks WR, Richarson S, Spiegelhalter DJ, editors. Markov Chain Monte Carlo in Practice, New York: Chapman and Hall/CRC, 1995. https://doi.org/10.1201/b14835
[29]	Yu SY (2021) MatCalib: A Matlab software package for Bayesian calibration of radiocarbon ages subject to temporal order constraints. Mendeley Data, V1. https://doi.org/10.17632/rx478cbpm5.1
[30]	Lougheed BC, Obrochta SP (2016) MatCal: Open source Bayesian ¹⁴C age calibration in MatLab. J Open Res Softw 4: p.e42. http://doi.org/10.5334/jors.130
[31]	The Institute of Archaeology (1992) Radiocarbon Dates in Chinese Archaeology (1965-1991), Beijing: Cultural Relics Publishing House, 488.
[32]	Long T, Wagner M, Tarasov PE (2017) A Bayesian analysis of radiocarbon dates from prehistoric sites in the Haidai Region, East China, for evaluation of the archaeological chronology. J Archaeol Sci Rep 12: 81-90. https://doi.org/10.1016/j.jasrep.2017.01.024 doi: 10.1016/j.jasrep.2017.01.024
[33]	Yu SY, Berglund BE, Sandgren P, et al. (2005) Holocene palaeoecology along the Blekinge coast, SE Sweden, and implications for climate and sea-level changes. Holocene 15: 278-292. https://doi.org/10.1191/0959683605hl792rp doi: 10.1191/0959683605hl792rp
[34]	Yu SY, Berglund B, Sandgren P, et al. (2007) Evidence for a rapid sea-level rise 7600 yr ago. Geology 35: 891-894. https://doi.org/10.1130/G23859A.1 doi: 10.1130/G23859A.1
[35]	Alves EQ, Macario K, Ascough P, et al. (2018) The worldwide marine radiocarbon reservoir effect: definitions, mechanisms, and prospects. Rev Geophys 56: 278-305. https://doi.org/10.1002/2017RG000588 doi: 10.1002/2017RG000588
[36]	Blaauw M (2010) Methods and code for 'classical' age-modelling of radiocarbon sequences. Quat Geochronol 5: 512-518. https://doi.org/10.1016/j.quageo.2010.01.002 doi: 10.1016/j.quageo.2010.01.002
[37]	Bronk Ramsey C (2008) Deposition models for chronological records. Quat Sci Rev 27: 42-60. https://doi.org/10.1016/j.quascirev.2007.01.019 doi: 10.1016/j.quascirev.2007.01.019
[38]	Lougheed BC, Obrochta S (2019) A papid, deterministic age-depth modeling routine for geological sequences with inherent depth uncertainty. Paleoceanography Paleoclimatology 34: 122-133. https://doi.org/10.1029/2018PA003457 doi: 10.1029/2018PA003457
[39]	Haslett J, Parnell A (2008) A simple monotone process with application to radiocarbon-dated depth chronologies. J R Stat Soc 57: 399-418. https://doi.org/10.1111/j.1467-9876.2008.00623.x doi: 10.1111/j.1467-9876.2008.00623.x
[40]	Blaauw M, Christen JA (2011) Flexible paleoclimate age-depth models using an autoregressive gamma process. Bayesian Anal 6: 457-474. https://doi.org/10.1214/11-BA618 doi: 10.1214/11-BA618

geosci-08-01-002-s001.pdf
geosci-08-01-002-s002.zip

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)