What drives the glacial-interglacial cycle? A Bayesian solution to a long-standing model selection problem.
Richard Wilkinson (University of Nottingham)
Friday 7th November, 2014 15:00-16:00 Maths 203
The current ice age began approximately 3 Myr ago. Since then, the climate has fluctuated between glacial and inter-glacial periods, with the current inter-glacial period having lasted approximately 12 kyr. Scientists aim to understand the dynamics of this cycle using low-order oscillating dynamical models, which they drive using the known solar forcing. Many different studies have argued for the primacy of different aspects of the solar forcing, or for different dynamical systems models, by comparing data from ice-cores to (often hand-tuned) model predictions. Computational intractability has meant that heuristic arguments are usually used to argue for the superiority of a particular model or regime, rather than any form of principled statistical inference.
In this talk, I will describe how recent advances in Monte Carlo methodology, particularly the SMC^2 methodology of Chopin et al. 2012, allow us to give an answer to the long running debate about the impact of the solar forcing and whether it is possible to choose between models (given the paucity of the data) by estimating parameter posteriors and Bayes factors. In order to make this approach feasible, careful design of the proposal distributions is necessary, with Brownian bridge type proposals proving to be successful in this setting. I will show that our answer is sensitive to the age model used to date the data, and will argue that in order to make progress it is necessary to solve the dating, climate reconstruction, model calibration and model selection problems jointly in a single coherent analysis. I will describe promising preliminary results in this direction and suggest what remains to be done before this can be scaled up to analyse complex multi-core datasets.