  A major goal in paleoclimate science is to reconstruct historical climates
using proxies for climate variables such as those observed in sediment cores,
and in the process learn about climate dynamics. This is hampered by
uncertainties in how sediment core depths relate to ages, how proxy quantities
relate to climate variables, how climate models are specified, and the values
of parameters in climate models. Quantifying these uncertainties is key in
drawing well founded conclusions. Analyses are often performed in separate
stages with, for example, a sediment core's depth-age relation being estimated
as 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 misleading
conclusions. We develop a joint inferential approach for climate
reconstruction, model calibration, and age model estimation. We focus on the
glacial-interglacial cycle over the past 780 kyr, analysing two sediment cores
that span this range. Our age estimates are largely in agreement with previous
studies, but provides the full joint specification of all uncertainties,
estimation of model parameters, and the model evidence. By sampling plausible
chronologies from the posterior distribution, we demonstrate that downstream
scientific conclusions can differ greatly both between different sampled
chronologies, and in comparison with conclusions obtained in the complete joint
inferential analysis. We conclude that multi-stage analyses are insufficient
when dealing with uncertainty, and that to draw sound conclusions the full
joint inferential analysis must be performed.
