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

TLDR

Establishing a monotone age–depth chronology for lake sediment cores using radiocarbon dates at selected depths. To develop a simple continuous Markov monotone stochastic process for inference on partially observed monotone processes. The method models sedimentation as a piecewise‑linear continuous Markov monotone process with independent gamma increments in a Poisson framework, enabling efficient conditional simulation via a Tweedie reparameterization.

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.