A probabilistic Pliocene–Pleistocene stack of benthic δ18O using a profile hidden Markov model

We present a 5-Myr probabilistic stack, which we name the Prob-stack. It is constructed from 180 globally distributed benthic δ18O records using a profile hidden Markov model (HMM). Benthic stacks have been extensively employed to estimate ages in marine sediment cores and lead–lag relationships between paleoclimate proxies. Because this stack is probabilistic, it incorporates the variability among multiple records used in its construction and the uncertainty in alignments of records to the stack that have not been included in previous studies. It represents the uncertainty stemming from these two sources using a normal distribution with mean and variance in benthic δ18O at each point in the stack. In doing so, Prob-stack captures the time-varying mean and variance of benthic δ18O in the global ocean, which allows for better assessment of the uncertainty in records’ relative ages, such as lead–lag relationships. Algorithms are included.