The reassignment phase of the variable dimension posterior algorithm that we have used can only reassign elements to existing regions that were created during the first phase. It could be modified to allow for the birth and death of regions.
For each region we have used the Kullback-Leibler distance as a loss function to estimate the point estimate. The point estimate is therefore a good representative in terms of predictive performance for the models contained within a region. However, this method of point estimation does not take into account the number of parameters in the model estimated. This problem was not extreme5 in our examples because we did not estimate the parameters for each segment. If we were to do so, and used an infinite posterior sample size, then we would find that the point estimate for each region would contain a change-point between every datum. While this does not affect predictive performance, it does affect the human comprehension property that we require. A general, objective means of achieving parsimony in the number of parameters is an area that requires more investigation.