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Classical dynamic Bayesian networks (DBNs) are based on the homogeneous Markov assumption and cannot deal with non-homogeneous temporal processes. Various approaches to relax the homogeneity assumption have recently been proposed. The present paper presents a combination of a Bayesian network with conditional probabilities in the linear Gaussian family, and a Bayesian multiple changepoint process, where the number and location of the changepoints are sampled from the posterior distribution with MCMC. Our work improves four aspects of an earlier conference paper: it contains a comprehensive and self-contained exposition of the methodology; it discusses the problem of spurious feedback loops in network reconstruction; it contains a comprehensive comparative evaluation of the network reconstruction accuracy on a set of synthetic and real-world benchmark problems, based on a novel discrete changepoint process; and it suggests new and improved MCMC schemes for sampling both the network structures and the changepoint configurations from the posterior distribution. The latter study compares RJMCMC, based on changepoint birth and death moves, with two dynamic programming schemes that were originally devised for Bayesian mixture models. We demonstrate the modifications that have to be made to allow for changing network structures, and the critical impact that the prior distribution on changepoint configurations has on the overall computational complexity.