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A major goal in paleoclimate science is to reconstruct historical climatesusing proxies for climate variables such as those observed in sediment cores,and in the process learn about climate dynamics. This is hampered byuncertainties in how sediment core depths relate to ages, how proxy quantitiesrelate to climate variables, how climate models are specified, and the valuesof parameters in climate models. Quantifying these uncertainties is key indrawing well founded conclusions. Analyses are often performed in separatestages with, for example, a sediment core's depth-age relation being estimatedas stage one, then fed as an input to calibrate climate models as stage two.Here, we show that such "multi-stage" approaches can lead to misleadingconclusions. We develop a joint inferential approach for climatereconstruction, model calibration, and age model estimation. We focus on theglacial-interglacial cycle over the past 780 kyr, analysing two sediment coresthat span this range. Our age estimates are largely in agreement with previousstudies, but provides the full joint specification of all uncertainties,estimation of model parameters, and the model evidence. By sampling plausiblechronologies from the posterior distribution, we demonstrate that downstreamscientific conclusions can differ greatly both between different sampledchronologies, and in comparison with conclusions obtained in the complete jointinferential analysis. We conclude that multi-stage analyses are insufficientwhen dealing with uncertainty, and that to draw sound conclusions the fulljoint inferential analysis must be performed.

Quantifying Age and Model Uncertainties in Paleoclimate Data and Dynamical Climate Models with a Joint Inferential Analysis