Bayesian Inference Gaussian Process Multiproxy Alignment of Continuous Signals (BIGMACS): Applications for Paleoceanography
We first introduce a novel profile-based alignment algorithm, the multiple continuous Signal Alignment algorithm with Gaussian Process Regression profiles (SA-GPR). SA-GPR addresses the limitations of currently available signal alignment methods by adopting a hybrid of the particle smoothing and Markov-chain Monte Carlo (MCMC) algorithms to align signals, and by applying the Gaussian process regression to construct profiles to be aligned continuously. SA-GPR shares all the strengths of the existing alignment algorithms that depend on profiles but is more exact in the sense that profiles do not need to be discretized as sequential bins. The uncertainty of performance over the resolution of such bins is thereby eliminated. This methodology produces alignments that are consistent, that regularize extreme cases, and that properly reflect the inherent uncertainty. Then we extend SA-GPR to a specific problem in the field of paleoceanography with a method called Bayesian Inference Gaussian Process Multiproxy Alignment of Continuous Signals (BIGMACS). The goal of BIGMACS is to infer continuous ages for ocean sediment cores using two classes of age proxies: proxies that explicitly return calendar ages (e.g., radiocarbon) and those used to synchronize ages in multiple marine records (e.g., an oxygen isotope based marine proxy known as benthic $δ^{18}{\rm O}$). BIGMACS integrates these two proxies by iteratively performing two steps: profile construction from benthic $δ^{18}{\rm O}$ age models and alignment of each core to the profile also reflecting radiocarbon dates. We use BIGMACS to construct a new Deep Northeastern Atlantic stack (i.e., a profile from a particular benthic $δ^{18}{\rm O}$ records) of five ocean sediment cores. We conclude by constructing multiproxy age models for two additional cores from the same region by aligning them to the stack.