Supplementary Material to "bayesian Age Models and Stacks: Combining Age Inferences from Radiocarbon and Benthic Δ18o Stratigraphic Alignment"

Supplement S1. Transition ModelAt a given core depth , the transition model returns the probability of an age sample and the sedimentation rate state , given the normalized sedimentation rate and the previous sedimentation rate state +1 : ( , | +1 , +1 , , , +1 , ) = 1 ( | +1 , ) 2 ( | +1 , ; , +1 , ).Here 1 ( | +1 , ) returns the probability of transitioning from +1 to .The variable is a matrix containing the probabilities of transitioning from each state to all other states.The three sedimentation rate states are expansion, steady, and contraction and have respective normalized sedimentation rate ranges of (0,0.9220),[0.9220,1.0850),and [1.0850, ∞). can either remain fixed or can be optimized during age model construction.The second term 2 ( | +1 , ; , +1 , ) returns the probability of the required sedimentation rate and is calculated using the log-normal mixture distribution fit to the normalized sedimentation rates from Lin et al., (2014): 2 ( | +1 , ; , +1 , ) ∝ (∑ • ( +1 - • ( +1 - ) | , ) 2 =1 ) • 1 { +1 - •( +1 - ) ∈ } ( ).