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A simple monotone process with application to radiocarbon‐dated depth chronologies
Author(s) -
Haslett John,
Parnell Andrew
Publication year - 2008
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/j.1467-9876.2008.00623.x
Subject(s) - monotone polygon , mathematics , inference , simple (philosophy) , radiocarbon dating , computer science , geology , geometry , artificial intelligence , paleontology , philosophy , epistemology
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 ( 14 C) dating at a subset of depths. We use the process to model the stochastically varying rate of sedimentation.