  Ice cores provide insight into the past climate over many millennia. Due to
ice compaction, the raw data for any single core are irregular in time.
Multiple cores have different irregularities; jointly these series are
misaligned. After processing, such data are made available to researchers as
regular time series: a data product. Typically, these cores are independently
processed. In this paper, we consider a fast Bayesian method for the joint
processing of multiple irregular series. This is shown to be more efficient.
Further, our approach permits a realistic modelling of the impact of the
multiple sources of uncertainty. The methodology is illustrated with the
analysis of a pair of ice cores (GISP2 and GRIP). Our data products, in the
form of marginal posterior distributions on an arbitrary temporal grid, are
finite Gaussian mixtures. We can also produce sample paths from the joint
posterior distribution to study non-linear functionals of interest. More
generally, the concept of joint analysis via hierarchical Gaussian process
model can be widely extended as the models used can be viewed within the larger
context of continuous space-time processes.
