Dual Proxy Gaussian Process Stack: Integrating Benthic
$?^{18}{\rm{O}}$ and Radiocarbon Proxies for Inferring Ages on Ocean
Sediment Cores
Academic Article

Ages in ocean sediment cores are often inferred using either benthic
${\delta}^{18}{\rm{O}}$ or planktonic ${}^{14}{\rm{C}}$ of foraminiferal
calcite. Existing probabilistic dating methods infer ages in two distinct
approaches: ages are either inferred directly using radionuclides, e.g. Bacon
[Blaauw and Christen (2011)]; or indirectly based on the alignment of records,
e.g. HMM-Match [Lin et al. (2014)]. In this paper, we introduce a novel
algorithm for integrating these two approaches by constructing Dual Proxy
Gaussian Process (DPGP) stacks, which represent a probabilistic model of
benthic ${\delta}^{18}{\rm{O}}$ change (and its timing) based on a set of
cores. While a previous stack construction algorithm, HMM-Match, uses a
discrete age inference model based on Hidden Markov models (HMMs) [Durbin et
al. (1998)] and requires a number of records enough to sufficiently cover all
its ages, DPGP stacks with time-varying variances are constructed with
continuous ages obtained by particle smoothing [Doucet et al. (2001); Klaas et
al. (2006)] and Markov-chain Monte Carlo (MCMC) [Peters (2008)] algorithms, and
can be derived from a small number of records by applying the Gaussian process
regression [Rasmussen and Williams (2005)]. As an example of the stacking
method, we construct a local stack from 6 cores in the deep northeastern
Atlantic Ocean and compare it to a deterministically constructed
${\delta}^{18}{\rm{O}}$ stack of 58 cores from the deep North Atlantic
[Lisiecki and Stern (2016)]. We also provide two examples of how dual proxy
alignment ages can be inferred by aligning additional cores to the stack.