  We generalize the approach of Liu and Lawrence (1999) for multiple
changepoint problems where the number of changepoints is unknown. The approach
is based on dynamic programming recursion for efficient calculation of the
marginal probability of the data with the hidden parameters integrated out. For
the estimation of the hyperparameters, we propose to use Monte Carlo EM when
training data are available. We argue that there is some advantages of using
samples from the posterior which takes into account the uncertainty of the
changepoints, compared to the traditional MAP estimator, which is also more
expensive to compute in this context. The samples from the posterior obtained
by our algorithm are independent, getting rid of the convergence issue
associated with the MCMC approach. We illustrate our approach on limited
simulations and some real data set.
