Analyzing Statistical Age Models to Determine the Equivalent Dose and Burial Age Using a Markov Chain Monte Carlo Method

Adamiec G, Heer AJ and Bluszcz A, 2012. Statistics of count numbers from a photomultiplier tube and its implications for error estimation. Radiation Measurements 47(9): 746–751, DOI 10.1016/j.radmeas.2011.12.009. AdamiecG HeerAJ BluszczA 2012 Statistics of count numbers from a photomultiplier tube and its implications for error estimation Radiation Measurements 47 9 746 751 10.1016/j.radmeas.2011.12.009 Open DOISearch in Google Scholar

Annis J, Miller BJ and Palmeri TJ, 2017. Bayesian inference with Stan: A tutorial on adding custom distributions. Behaviour research methods 49(3): 863–886, DOI 10.3758/s13428-016-0746-9. AnnisJ MillerBJ PalmeriTJ 2017 Bayesian inference with Stan: A tutorial on adding custom distributions Behaviour research methods 49 3 863 886 10.3758/s13428-016-0746-9 514911827287444 Open DOISearch in Google Scholar

Arnold LJ, Bailey RM and Tucker GE, 2007. Statistical treatment of fluvial dose distributions from southern Colorado arroyo deposits. Quaternary Geochronology 2(1–4): 162–167, DOI 10.1016/j.quageo.2006.05.003. ArnoldLJ BaileyRM TuckerGE 2007 Statistical treatment of fluvial dose distributions from southern Colorado arroyo deposits Quaternary Geochronology 2 1–4 162 167 10.1016/j.quageo.2006.05.003 Open DOISearch in Google Scholar

Arnold LJ and Roberts RG, 2009. Stochastic modelling of multi-grain equivalent dose (D_e) distributions: Implications for OSL dating of sediment mixtures. Quaternary Geochronology 4(3): 204–230, DOI 10.1016/j.quageo.2008.12.001. ArnoldLJ RobertsRG 2009 Stochastic modelling of multi-grain equivalent dose (D_e) distributions: Implications for OSL dating of sediment mixtures Quaternary Geochronology 4 3 204 230 10.1016/j.quageo.2008.12.001 Open DOISearch in Google Scholar

Arnold LJ, Roberts RG, Galbraith RF and DeLong SB, 2009. A revised burial dose estimation procedure for optical dating of young and modern-age sediments. Quaternary Geochronology 4(4): 306–325, DOI 10.1016/j.quageo.2009.02.017. ArnoldLJ RobertsRG GalbraithRF DeLongSB 2009 A revised burial dose estimation procedure for optical dating of young and modern-age sediments Quaternary Geochronology 4 4 306 325 10.1016/j.quageo.2009.02.017 Open DOISearch in Google Scholar

Bayliss A and Ramsey CB, 2004. Pragmatic Bayesians: a decade of integrating radiocarbon dates into chronological models. Lecture Notes in Statistics, Springer, London. DOI 10.1007/978-1-4471-0231-1_2. BaylissA RamseyCB 2004 Pragmatic Bayesians: a decade of integrating radiocarbon dates into chronological models Lecture Notes in Statistics, Springer London 10.1007/978-1-4471-0231-1_2 Open DOISearch in Google Scholar

Bluszcz A, Adamiec G and Heer AJ, 2015. Estimation of equivalent dose and its uncertainty in the OSL SAR protocol when count numbers do not follow a Poisson distribution. Radiation Measurements 81: 46–54, DOI 10.1016/j.radmeas.2015.01.004. BluszczA AdamiecG HeerAJ 2015 Estimation of equivalent dose and its uncertainty in the OSL SAR protocol when count numbers do not follow a Poisson distribution Radiation Measurements 81 46 54 10.1016/j.radmeas.2015.01.004 Open DOISearch in Google Scholar

Brill D, Jankaew K and Brückner H, 2015. Holocene evolution of Phra Thong's beach-ridge plain (Thailand) — Chronology, processes and driving factors. Geomorphology 245: 117–134, DOI 10.1016/j.geomorph.2015.05.035. BrillD JankaewK BrücknerH 2015 Holocene evolution of Phra Thong's beach-ridge plain (Thailand) — Chronology, processes and driving factors Geomorphology 245 117 134 10.1016/j.geomorph.2015.05.035 Open DOISearch in Google Scholar

Christophe C, Philippe A, Guérin G, Mercie N and Guibert P, 2018. Bayesian approach to OSL dating of poorly bleached sediment samples: Mixture Distribution Models for Dose (MD²). Radiation Measurements 108: 59–73, DOI 10.1016/j.radmeas.2017.10.007. ChristopheC PhilippeA GuérinG MercieN GuibertP 2018 Bayesian approach to OSL dating of poorly bleached sediment samples: Mixture Distribution Models for Dose (MD²) Radiation Measurements 108 59 73 10.1016/j.radmeas.2017.10.007 Open DOISearch in Google Scholar

Combès B and Philippe A, 2017. Bayesian analysis of individual and systematic multiplicative errors for estimating ages with stratigraphic constraints in optically stimulated luminescence dating. Quaternary Geochronology 39: 24–34, DOI 10.1016/j.quageo.2017.02.003. CombèsB PhilippeA 2017 Bayesian analysis of individual and systematic multiplicative errors for estimating ages with stratigraphic constraints in optically stimulated luminescence dating Quaternary Geochronology 39 24 34 10.1016/j.quageo.2017.02.003 Open DOISearch in Google Scholar

Combès B, Philippe A, Lanos P, Mercier N, Tribolo C, Guerin G, Guibert P and Lahaye C, 2015. A Bayesian central equivalent dose model for optically stimulated luminescence dating. Quaternary Geochronology 28: 62–70, DOI 10.1016/j.quageo.2015.04.001. CombèsB PhilippeA LanosP MercierN TriboloC GuerinG GuibertP LahayeC 2015 A Bayesian central equivalent dose model for optically stimulated luminescence dating Quaternary Geochronology 28 62 70 10.1016/j.quageo.2015.04.001 Open DOISearch in Google Scholar

Cunningham AC, Evans M and Knight J, 2015b. Quantifying bleaching for zero-age fluvial sediment: A Bayesian approach. Radiation Measurements 81: 55–61, DOI 10.1016/j.radmeas.2015.04.007. CunninghamAC EvansM KnightJ 2015b Quantifying bleaching for zero-age fluvial sediment: A Bayesian approach Radiation Measurements 81 55 61 10.1016/j.radmeas.2015.04.007 Open DOISearch in Google Scholar

Cunningham AC and Wallinga J, 2012. Realizing the potential of fluvial archives using robust OSL chronologies. Quaternary Geochronology 12: 98–106, DOI 10.1016/j.quageo.2012.05.007. CunninghamAC WallingaJ 2012 Realizing the potential of fluvial archives using robust OSL chronologies Quaternary Geochronology 12 98 106 10.1016/j.quageo.2012.05.007 Open DOISearch in Google Scholar

Cunningham AC, Wallinga J, Hobo N, Versendaal AJ, Makaske B and Middelkoop H, 2015a. Re-evaluating luminescence burial doses and bleaching of fluvial deposits using Bayesian computational statistics. Earth Surface Dynamics 3(1): 55–65, DOI 10.5194/esurf-3-55-2015. CunninghamAC WallingaJ HoboN VersendaalAJ MakaskeB MiddelkoopH 2015a Re-evaluating luminescence burial doses and bleaching of fluvial deposits using Bayesian computational statistics Earth Surface Dynamics 3 1 55 65 10.5194/esurf-3-55-2015 Open DOISearch in Google Scholar

Galbraith RF and Green PF, 1990. Estimating the component ages in a finite mixture. Nuclear Tracks and Radiation Measurements 17(3): 197–206, DOI 10.1016/1359-0189(90)90035-V. GalbraithRF GreenPF 1990 Estimating the component ages in a finite mixture Nuclear Tracks and Radiation Measurements 17 3 197 206 10.1016/1359-0189(90)90035-V Open DOISearch in Google Scholar

Galbraith RF and Roberts RG, 2012. Statistical aspects of equivalent dose and error calculation and display in OSL dating: An overview and some recommendations. Quaternary Geochronology 11: 1–27, DOI 10.1016/j.quageo.2012.04.020. GalbraithRF RobertsRG 2012 Statistical aspects of equivalent dose and error calculation and display in OSL dating: An overview and some recommendations Quaternary Geochronology 11 1 27 10.1016/j.quageo.2012.04.020 Open DOISearch in Google Scholar

Galbraith RF, Roberts RG, Laslett GM, Yoshida H and Olley JM, 1999. Optical dating of single and multiple grains of quartz from Jinmium rock shelter, northern Australia: Part I, experimental design and statistical models. Archaeometry 41(2): 339–364, DOI 10.1111/j.1475-4754.1999.tb00987.x. GalbraithRF RobertsRG LaslettGM YoshidaH OlleyJM 1999 Optical dating of single and multiple grains of quartz from Jinmium rock shelter, northern Australia: Part I, experimental design and statistical models Archaeometry 41 2 339 364 10.1111/j.1475-4754.1999.tb00987.x Open DOISearch in Google Scholar

Galbraith RF, Roberts RG and Yoshida H, 2005. Error variation in OSL palaeodose estimates from single aliquots of quartz: a factorial experiment. Radiation Measurements 39(3): 289–307, DOI 10.1016/j.radmeas.2004.03.023. GalbraithRF RobertsRG YoshidaH 2005 Error variation in OSL palaeodose estimates from single aliquots of quartz: a factorial experiment Radiation Measurements 39 3 289 307 10.1016/j.radmeas.2004.03.023 Open DOISearch in Google Scholar

Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A and Rubin DB, 2014. Bayesian data analysis. Boca Raton, FL, CRC press. GelmanA CarlinJB SternHS DunsonDB VehtariA RubinDB 2014 Bayesian data analysis Boca Raton, FL CRC press 10.1201/b16018 Search in Google Scholar

Gelman A, Lee D and Guo JQ, 2015. Stan: A probabilistic programming language for Bayesian inference and optimization. Journal of Educational and Behavioral Statistics 40(5): 530–543, DOI 10.3102/1076998615606113. GelmanA LeeD GuoJQ 2015 Stan: A probabilistic programming language for Bayesian inference and optimization Journal of Educational and Behavioral Statistics 40 5 530 543 10.3102/1076998615606113 Open DOISearch in Google Scholar

Gelman A and Rubin DB, 1992. Inference from iterative simulation using multiple sequences. Statistical Science 7(4): 457–472, DOI 10.1214/ss/1177011136. GelmanA RubinDB 1992 Inference from iterative simulation using multiple sequences Statistical Science 7 4 457 472 10.1214/ss/1177011136 Open DOISearch in Google Scholar

Guérin G, Christophe C, Philippe A, Murray AS, Thomsen KJ, Tribolo C, Urbanova P, Jain M, Guibert P, Mercier N, Kreutzer S and Lahaye C, 2017. Absorbed dose, equivalent dose, measured dose rates and implications for OSL age estimates: Introducing the Average Dose Model. Quaternary Geochronology 41: 163–173, DOI 10.1016/j.quageo.2017.04.002. GuérinG ChristopheC PhilippeA MurrayAS ThomsenKJ TriboloC UrbanovaP JainM GuibertP MercierN KreutzerS LahayeC 2017 Absorbed dose, equivalent dose, measured dose rates and implications for OSL age estimates: Introducing the Average Dose Model Quaternary Geochronology 41 163 173 10.1016/j.quageo.2017.04.002 Open DOISearch in Google Scholar

Guérin G, Combès B, Lahaye C, Thomsen KJ, Tribolo C, Urbanova P, Guibert P, Mercier N and Vallada H, 2015. Testing the accuracy of a Bayesian central-dose model for single-grain OSL, using known-age samples. Radiation Measurements 81: 62–70, DOI 10.1016/j.radmeas.2015.04.002. GuérinG CombèsB LahayeC ThomsenKJ TriboloC UrbanovaP GuibertP MercierN ValladaH 2015 Testing the accuracy of a Bayesian central-dose model for single-grain OSL, using known-age samples Radiation Measurements 81 62 70 10.1016/j.radmeas.2015.04.002 Open DOISearch in Google Scholar

Huntriss A, 2008. A Bayesian analysis of luminescence dating. Doctoral dissertation, Durham University. HuntrissA 2008 A Bayesian analysis of luminescence dating Doctoral dissertation, Durham University Search in Google Scholar

Jacobs Z, Duller GAT and Wintle AG, 2006. Interpretation of single grain D_e distributions and calculation of D_e. Radiation Measurements 41(3): 264–277, DOI 10.1016/j.radmeas.2005.07.027. JacobsZ DullerGAT WintleAG 2006 Interpretation of single grain D_e distributions and calculation of D_e Radiation Measurements 41 3 264 277 10.1016/j.radmeas.2005.07.027 Open DOISearch in Google Scholar

Kunz A, Pflanz D, Weniger T, Urban B, Krüger F, Chen YG, 2013. Optically stimulated luminescence dating of young fluvial deposits of the Middle Elbe River Flood Plains using different age models. Geochronometria 41(1): 36–56, DOI 10.2478/s13386-013-0140-7. KunzA PflanzD WenigerT UrbanB KrügerF ChenYG 2013 Optically stimulated luminescence dating of young fluvial deposits of the Middle Elbe River Flood Plains using different age models Geochronometria 41 1 36 56 10.2478/s13386-013-0140-7 Open DOISearch in Google Scholar

Lanos P and Philippe A, 2015. Hierarchical Bayesian modeling for combining Dates in archaeological context. Journal de la société française de statistique 158(2): 72–88. LanosP PhilippeA 2015 Hierarchical Bayesian modeling for combining Dates in archaeological context Journal de la société française de statistique 158 2 72 88 Search in Google Scholar

Li B, 2007. A note on estimating the error when subtracting background counts from weak OSL signals. Ancient TL 25(1): 9–14. LiB 2007 A note on estimating the error when subtracting background counts from weak OSL signals Ancient TL 25 1 9 14 Search in Google Scholar

Li B, Jacobs Z, Roberts RG, Galbraith R and Peng, J, 2017. Variability in quartz OSL signals caused by measurement uncertainties: Problems and solutions. Quaternary Geochronology 41: 11–25, DOI 10.1016/j.quageo.2017.05.006. LiB JacobsZ RobertsRG GalbraithR PengJ 2017 Variability in quartz OSL signals caused by measurement uncertainties: Problems and solutions Quaternary Geochronology 41 11 25 10.1016/j.quageo.2017.05.006 Open DOISearch in Google Scholar

Mercier N, Kreutzer S, Christophe C, Guérin G, Guibert P, Lahaye C, Lanos P, Philippe P and Tribolo C, 2016. Bayesian statistics in luminescence dating: The “baSAR”-model and its implementation in the R package “Luminescence”. Ancient TL 34(2): 14–21. MercierN KreutzerS ChristopheC GuérinG GuibertP LahayeC LanosP PhilippeP TriboloC 2016 Bayesian statistics in luminescence dating: The “baSAR”-model and its implementation in the R package “Luminescence” Ancient TL 34 2 14 21 Search in Google Scholar

Millard AR, 2004. Taking Bayes beyond radiocarbon: Bayesian approaches to some other chronometric methods. Lecture Notes in Statistics, Springer, London. DOI 10.1007/978-1-4471-0231-1_11. MillardAR 2004 Taking Bayes beyond radiocarbon: Bayesian approaches to some other chronometric methods Lecture Notes in Statistics, Springer London 10.1007/978-1-4471-0231-1_11 Open DOISearch in Google Scholar

Murray AS and Wintle AG, 2000. Luminescence dating of quartz using an improved single-aliquot regenerative-dose protocol. Radiation Measurements 32(1): 57–73, DOI 10.1016/S1350-4487(99)00253-X. MurrayAS WintleAG 2000 Luminescence dating of quartz using an improved single-aliquot regenerative-dose protocol Radiation Measurements 32 1 57 73 10.1016/S1350-4487(99)00253-X Open DOISearch in Google Scholar

Olley JM, Roberts RG, Yoshida H and Bowler JM, 2006. Single-grain optical dating of grave-infill associated with human burials at Lake Mungo, Australia. Quaternary Science Reviews 25(19–20): 2469–2474, DOI 10.1016/j.quascirev.2005.07.022. OlleyJM RobertsRG YoshidaH BowlerJM 2006 Single-grain optical dating of grave-infill associated with human burials at Lake Mungo, Australia Quaternary Science Reviews 25 19–20 2469 2474 10.1016/j.quascirev.2005.07.022 Open DOISearch in Google Scholar

Peng J and Dong ZB, 2014. A simple Bayesian method for assessing the standard error of equivalent dose estimates. Ancient TL 32(2): 17–23. PengJ DongZB 2014 A simple Bayesian method for assessing the standard error of equivalent dose estimates Ancient TL 32 2 17 23 Search in Google Scholar

Peng J, Dong ZB and Han FQ, 2016a. Application of slice sampling method for optimizing OSL age models used for equivalent dose determination. Progress in Geography 35(1): 78–88. (in Chinese) PengJ DongZB HanFQ 2016a Application of slice sampling method for optimizing OSL age models used for equivalent dose determination Progress in Geography 35 1 78 88 (in Chinese) Search in Google Scholar

Peng J, Dong ZB and Han FQ, 2016b. Optically stimulated luminescence dating of sandy deposits from Gulang county at the southern margin of the Tengger Desert, China. Journal of Arid Land 8(1): 1–12, DOI 10.1007/s40333-015-0137-6. PengJ DongZB HanFQ 2016b Optically stimulated luminescence dating of sandy deposits from Gulang county at the southern margin of the Tengger Desert, China Journal of Arid Land 8 1 1 12 10.1007/s40333-015-0137-6 Open DOISearch in Google Scholar

Peng J, Dong ZB, Han FQ, Long H and Liu XJ, 2013. R package numOSL: numeric routines for optically stimulated luminescence dating. Ancient TL 31(2): 41–48. PengJ DongZB HanFQ LongH LiuXJ 2013 R package numOSL: numeric routines for optically stimulated luminescence dating Ancient TL 31 2 41 48 Search in Google Scholar

Peng J and Li B, 2017. Single-aliquot regenerative-dose (SAR) and standardised growth curve (SGC) equivalent dose determination in a batch model using the R package “numOSL”. Ancient TL 35(2): 32–53. PengJ LiB 2017 Single-aliquot regenerative-dose (SAR) and standardised growth curve (SGC) equivalent dose determination in a batch model using the R package “numOSL” Ancient TL 35 2 32 53 10.1016/j.radmeas.2016.09.006 Search in Google Scholar

Philippe A, Guérin G and Kreutzer S, 2019. BayLum - An R package for Bayesian analysis of OSL ages: An introduction. Quaternary Geochronology 49: 16–24, DOI 10.1016/j.quageo.2018.05.009. PhilippeA GuérinG KreutzerS 2019 BayLum - An R package for Bayesian analysis of OSL ages: An introduction Quaternary Geochronology 49 16 24 10.1016/j.quageo.2018.05.009 Open DOISearch in Google Scholar

Ramsey CB, 1995. Radiocarbon calibration and analysis of stratigraphy: the OxCal program. Radiocarbon 37(2): 425–430. RamseyCB 1995 Radiocarbon calibration and analysis of stratigraphy: the OxCal program Radiocarbon 37 2 425 430 10.1017/S0033822200030903 Search in Google Scholar

Ramsey C B, 2008. Deposition models for chronological records. Quaternary Science Reviews 27(1–2): 42–60, DOI 10.1016/j.quascirev.2007.01.019. RamseyCB 2008 Deposition models for chronological records Quaternary Science Reviews 27 1–2 42 60 10.1016/j.quascirev.2007.01.019 Open DOISearch in Google Scholar

Rhodes EJ, Ramsey CB, Outram Z, Batt C, Willis L, Dockrill S and Bond J, 2003. Bayesian methods applied to the interpretation of multiple OSL dates: high precision sediment ages from Old Scatness Broch excavations, Shetland Isles. Quaternary Science Reviews 22(10–13): 1231–1244, DOI 10.1016/S0277-3791(03)00046-5. RhodesEJ RamseyCB OutramZ BattC WillisL DockrillS BondJ 2003 Bayesian methods applied to the interpretation of multiple OSL dates: high precision sediment ages from Old Scatness Broch excavations, Shetland Isles Quaternary Science Reviews 22 10–13 1231 1244 10.1016/S0277-3791(03)00046-5 Open DOISearch in Google Scholar

Roberts RG, Galbraith RF, Yoshida H, Laslett GM and Olley JM, 2000. Distinguishing dose populations in sediment mixtures: a test of single-grain optical dating procedures using mixtures of laboratory-dosed quartz. Radiation Measurements 32(5–6): 459–465, DOI 10.1016/S1350-4487(00)00104-9. RobertsRG GalbraithRF YoshidaH LaslettGM OlleyJM 2000 Distinguishing dose populations in sediment mixtures: a test of single-grain optical dating procedures using mixtures of laboratory-dosed quartz Radiation Measurements 32 5–6 459 465 10.1016/S1350-4487(00)00104-9 Open DOISearch in Google Scholar

Schmidt S, Tsukamoto S, Salomon E, Frechen M and Hetzel R, 2012. Optical dating of alluvial deposits at the orogenic front of the Andean Precordillera (Mendoza, Argentina). Geochronometria 39(1): 62–75, DOI 10.2478/s13386-011-0050-5. SchmidtS TsukamotoS SalomonE FrechenM HetzelR 2012 Optical dating of alluvial deposits at the orogenic front of the Andean Precordillera (Mendoza, Argentina) Geochronometria 39 1 62 75 10.2478/s13386-011-0050-5 Open DOISearch in Google Scholar

Sivia DS, Burbidge C, Roberts RG and Bailey RM, 2004. A Bayesian approach to the evaluation of equivalent doses in sediment mixtures for luminescence dating. AIP Conference Proceedings 735(1): 305–311, DOI 10.1063/1.1835227. SiviaDS BurbidgeC RobertsRG BaileyRM 2004 A Bayesian approach to the evaluation of equivalent doses in sediment mixtures for luminescence dating AIP Conference Proceedings 735 1 305 311 10.1063/1.1835227 Open DOISearch in Google Scholar

Stan Development Team, 2018. RStan: the R interface to Stan. R package version 2.17.3. Stan Development Team 2018 RStan: the R interface to Stan R package version 2.17.3 10.2478/msd-2018-0003 Search in Google Scholar

Tamura T, Cunningham AC and Oliver TSN, 2019. Two-dimensional chronostratigraphic modelling of OSL ages from recent beach-ridge deposits, SE Australia. Quaternary Geochronology 49: 39–44, DOI 10.1016/j.quageo.2018.03.003. TamuraT CunninghamAC OliverTSN 2019 Two-dimensional chronostratigraphic modelling of OSL ages from recent beach-ridge deposits, SE Australia Quaternary Geochronology 49 39 44 10.1016/j.quageo.2018.03.003 Open DOISearch in Google Scholar

Thomsen, K.J., Murray, A.S., Bøtter-Jensen, L., 2005. Sources of variability in OSL dose measurements using single grains of quartz. Radiation Measurements 39(1): 47–61, DOI 10.1016/j.radmeas.2004.01.039. ThomsenK.J. MurrayA.S. Bøtter-JensenL. 2005 Sources of variability in OSL dose measurements using single grains of quartz Radiation Measurements 39 1 47 61 10.1016/j.radmeas.2004.01.039 Open DOISearch in Google Scholar

Zeeden C, Dietze M and Kreutzer S, 2018. Discriminating luminescence age uncertainty composition for a robust Bayesian modelling. Quaternary Geochronology 43: 30–39, DOI 10.1016/j.quageo.2017.10.001. ZeedenC DietzeM KreutzerS 2018 Discriminating luminescence age uncertainty composition for a robust Bayesian modelling Quaternary Geochronology 43 30 39 10.1016/j.quageo.2017.10.001 Open DOISearch in Google Scholar

Zink A, 2013. A coarse Bayesian approach to evaluate luminescence ages. Geochronometria 40(2): 90–100, DOI 10.2478/s13386-013-0105-x. ZinkA 2013 A coarse Bayesian approach to evaluate luminescence ages Geochronometria 40 2 90 100 10.2478/s13386-013-0105-x Open DOISearch in Google Scholar

Zink AJC, 2015. Bayesian analysis of luminescence measurements. Radiation Measurements 81: 71–77, DOI 10.1016/j.radmeas.2015.04.009. ZinkAJC 2015 Bayesian analysis of luminescence measurements Radiation Measurements 81 71 77 10.1016/j.radmeas.2015.04.009 Open DOISearch in Google Scholar