simple monotone process with application to radiocarbon-dated depth chronologies

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 variati...

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Bibliographic Details
Published inApplied statistics Vol. 57; no. 4; pp. 399 - 418
Main Authors Haslett, John, Parnell, Andrew
Format Journal Article
LanguageEnglish
Published Oxford, UK Oxford, UK : Blackwell Publishing Ltd 01.09.2008
Blackwell Publishing Ltd
Blackwell Publishing
Blackwell
Royal Statistical Society
Oxford University Press
SeriesJournal of the Royal Statistical Society Series C
Subjects
Online AccessGet full text
ISSN0035-9254
1467-9876
DOI10.1111/j.1467-9876.2008.00623.x

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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.
Bibliography:http://dx.doi.org/10.1111/j.1467-9876.2008.00623.x
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ISSN:0035-9254
1467-9876
DOI:10.1111/j.1467-9876.2008.00623.x