  A prevailing viewpoint in palaeoclimate science is that a single
palaeoclimate record contains insufficient information to discriminate between
most competing explanatory models. Results we present here suggest the
contrary. Using SMC^2 combined with novel Brownian bridge type proposals for
the state trajectories, we show that even with relatively short time series it
is possible to estimate Bayes factors to sufficient accuracy to be able to
select between competing models. The results show that Monte Carlo methodology
and computer power have now advanced to the point where a full Bayesian
analysis for a wide class of conceptual climate models is now possible. The
results also highlight a problem with estimating the chronology of the climate
record prior to further statistical analysis, a practice which is common in
palaeoclimate science. Using two datasets based on the same record but with
different estimated chronologies results in conflicting conclusions about the
importance of the orbital forcing on the glacial cycle, and about the internal
dynamics generating the glacial cycle, even though the difference between the
two estimated chronologies is consistent with dating uncertainty. This
highlights a need for chronology estimation and other inferential questions to
be addressed in a joint statistical procedure.
