Bayesian inference for palaeoclimate with time uncertainty and stochastic volatility

We propose and fit a Bayesian model to infer palaeoclimate over several thousand years. The data that we use arise as ancient pollen counts taken from sediment cores together with radiocarbon dates which provide (uncertain) ages. When combined with a modern pollen-climate data set, we can calibrate ancient pollen into ancient climate. We use a normal-inverse Gaussian process prior to model the stochastic volatility of palaeoclimate over time, and we present a novel modularized Markov chain Monte Chain algorithm to enable fast computation. We illustrate our approach with a case-study from Sluggan Moss, Northern Ireland, and provide an R package, Bclim, for use at other sites.