A Simple Monotone Process with Application to Radiocarbon-Dated Depth Chronologies

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.

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