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A simple monotone process with application to radiocarbon‐dated depth chronologies

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  • John Haslett
  • Andrew Parnell

Abstract

Summary. We propose a new and simple continuous Markov monotone stochastic process and use it to make inference on a partially observed monotone stochastic process. The process is piecewise linear, based on additive independent gamma increments arriving in a Poisson fashion. An independent increments variation allows very simple conditional simulation of sample paths given known values of the process. We take advantage of a reparameterization involving the Tweedie distribution to provide efficient computation. The motivating problem is the establishment of a chronology for samples taken from lake sediment cores, i.e. the attribution of a set of dates to samples of the core given their depths, knowing that the age–depth relationship is monotone. The chronological information arises from radiocarbon (14C) dating at a subset of depths. We use the process to model the stochastically varying rate of sedimentation.

Suggested Citation

  • John Haslett & Andrew Parnell, 2008. "A simple monotone process with application to radiocarbon‐dated depth chronologies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(4), pages 399-418, September.
    • Handle: RePEc:bla:jorssc:v:57:y:2008:i:4:p:399-418
    DOI: 10.1111/j.1467-9876.2008.00623.x
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    References listed on IDEAS

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    1. Dunson, David B., 2005. "Bayesian Semiparametric Isotonic Regression for Count Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 618-627, June.
    2. J. O. Ramsay, 1998. "Estimating smooth monotone functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 365-375.
    3. Petros Dellaportas & Nial Friel & Gareth O. Roberts, 2006. "Bayesian model selection for partially observed diffusion models," Biometrika, Biometrika Trust, vol. 93(4), pages 809-825, December.
    4. Brezger, Andreas & Lang, Stefan, 2006. "Generalized structured additive regression based on Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 967-991, February.
    5. Brian Neelon & David B. Dunson, 2004. "Bayesian Isotonic Regression and Trend Analysis," Biometrics, The International Biometric Society, vol. 60(2), pages 398-406, June.
    6. Maarten Blaauw & J. Andrés Christen, 2005. "Radiocarbon peat chronologies and environmental change," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(4), pages 805-816, August.
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    Cited by:

    1. Enrico R Crema & Shinya Shoda, 2021. "A Bayesian approach for fitting and comparing demographic growth models of radiocarbon dates: A case study on the Jomon-Yayoi transition in Kyushu (Japan)," PLOS ONE, Public Library of Science, vol. 16(5), pages 1-26, May.
    2. Maarten Blaauw & J. Andrés Christen & Marco Antonio Aquino-López, 2020. "A Review of Statistics in Palaeoenvironmental Research," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(1), pages 17-31, March.
    3. Hernández, Armand & Sánchez-López, Guiomar & Pla-Rabes, Sergi & Comas-Bru, Laia & Parnell, Andrew & Cahill, Niamh & Geyer, Adelina & Trigo, Ricardo M & Giralt, Santiago, 2019. "A 2,000-year Bayesian NAO reconstruction from the Iberian Peninsula," Earth Arxiv p7ft6, Center for Open Science.

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