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We consider Bayesian analysis of a class of multiple changepoint models.While there are a variety of efficient ways to analyse these models if theparameters associated with each segment are independent, there are few generalapproaches for models where the parameters are dependent. Under the assumptionthat the dependence is Markov, we propose an efficient online algorithm forsampling from an approximation to the posterior distribution of the number andposition of the changepoints. In a simulation study, we show that theapproximation introduced is negligible. We illustrate the power of our approachthrough fitting piecewise polynomial models to data, under a model which allowsfor either continuity or discontinuity of the underlying curve at eachchangepoint. This method is competitive with, or out-performs, other methodsfor inferring curves from noisy data; and uniquely it allows for inference ofthe locations of discontinuities in the underlying curve.

Efficient Bayesian analysis of multiple changepoint models with dependence across segments