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

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  • John Haslett
  • Andrew Parnell

Abstract

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 (-super-14C) dating at a subset of depths. We use the process to model the stochastically varying rate of sedimentation. Copyright (c) 2008 Royal Statistical Society.

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.
  • Handle: RePEc:bla:jorssc:v:57:y:2008:i:4:p:399-418
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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. 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.
    3. 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.
    4. Brian Neelon & David B. Dunson, 2004. "Bayesian Isotonic Regression and Trend Analysis," Biometrics, The International Biometric Society, vol. 60(2), pages 398-406, June.
    5. 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.
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