This paper proposes a new Bayesian multiple change-point model which is based on the hidden Markov approach. The Dirichlet process hidden Markov model does not require the specification of the number of change-points a priori. Hence our model is robust to model specification in contrast to the fully parametric Bayesian model. We propose a general Markov chain Monte Carlo algorithm which only needs to sample the states around change-points. Simulations for a normal mean-shift model with known and unknown variance demonstrate advantages of our approach. Two applications, namely the coal-mining disaster data and the real United States Gross Domestic Product growth, are provided. We detect a single change-point for both the disaster data and US GDP growth. All the change-point locations and posterior inferences of the two applications are in line with existing methods.Comment: Published at http://dx.doi.org/10.1214/14-BA910 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/

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We provide a few technical details, additional simulation and empirical results in this supplementary appendices. In particular, supplementary Appendix B provides the discussion on the identification of latent variables and their coefficients. Supplementary Appendix C outlines the detailed MCMC estimation algorithm for the proposed model.We explain the model selection criterion for the latent dimension in supplementary Appendix D. Empirical results from other network relationships and robustness checks of model specifications are reported in supplementary Appendix E. We studies a counterfactual policy simulation to examine the multiplier effects from network interactions in Supplementary Appendix F. The goodness-of-fit of our network formation model to the real data is examined in supplementary Appendix G, while supplementary Appendix H depicts the time evolution of unobserved latent variables.

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