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

Joint Inference of Misaligned Irregular Time Series with Application to Greenland Ice Core Data