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

作者：John Haslett, Andrew Parnell · 发表于：Journal of the Royal Statistical Society Series C (Applied Statistics) · 年份：2008 · DOI：10.1111/j.1467-9876.2008.00623.x · 被引用次数：733 · 研究领域：Soil Geostatistics and Mapping、Hydrology and Sediment Transport Processes、Archaeology and ancient environmental studies

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.