  We show that the two-stage minimum description length (MDL) criterion widely
used to estimate linear change-point (CP) models corresponds to the marginal
likelihood of a Bayesian model with a specific class of prior distributions.
This allows results from the frequentist and Bayesian paradigms to be bridged
together. Thanks to this link, one can rely on the consistency of the number
and locations of the estimated CPs and the computational efficiency of
frequentist methods, and obtain a probability of observing a CP at a given
time, compute model posterior probabilities, and select or combine CP methods
via Bayesian posteriors. Furthermore, we adapt several CP methods to take
advantage of the MDL probabilistic representation. Based on simulated data, we
show that the adapted CP methods can improve structural break detection
compared to state-of-the-art approaches. Finally, we empirically illustrate the
usefulness of combining CP detection methods when dealing with long time series
and forecasting.
