  We outline a model and algorithm to perform inference on the palaeoclimate
and palaeoclimate volatility from pollen proxy data. We use a novel
multivariate non-linear non-Gaussian state space model consisting of an
observation equation linking climate to proxy data and an evolution equation
driving climate change over time. The link from climate to proxy data is
defined by a pre-calibrated forward model, as developed in Salter-Townshend and
Haslett (2012) and Sweeney (2012). Climatic change is represented by a
temporally-uncertain Normal-Inverse Gaussian Levy process, being able to
capture large jumps in multivariate climate whilst remaining temporally
consistent. The pre-calibrated nature of the forward model allows us to cut
feedback between the observation and evolution equations and thus integrate out
the state variable entirely whilst making minimal simplifying assumptions. A
key part of this approach is the creation of mixtures of marginal data
posteriors representing the information obtained about climate from each
individual time point. Our approach allows for an extremely efficient MCMC
algorithm, which we demonstrate with a pollen core from Sluggan Bog, County
Antrim, Northern Ireland.
