  In segmentation problems, inference on change-point position and model
selection are two difficult issues due to the discrete nature of change-points.
In a Bayesian context, we derive exact, non-asymptotic, explicit and tractable
formulae for the posterior distribution of variables such as the number of
change-points or their positions. We also derive a new selection criterion that
accounts for the reliability of the results. All these results are based on an
efficient strategy to explore the whole segmentation space, which is very
large. We illustrate our methodology on both simulated data and a comparative
genomic hybridisation profile.
