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

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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.
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Keywords: Compound Poisson; Monotone processes; Radiocarbon dating; Tweedie distribution; gamma distribution

Document Type: Research Article

Affiliations: Trinity College Dublin, Republic of Ireland

Publication date: 2008-09-01

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