Bayesian multiple changepoints detection for Markov jump processes

A Bayesian multiple changepoint model for the Markov jump process is formulated as a Markov double chain model in continuous time. Inference for this type of multiple changepoint model is based on a two-block Gibbs sampling scheme. We suggest a continuous-time version of forward-filtering backward-sampling (FFBS) algorithm for sampling the full trajectories of the latent Markov chain via inverse transformation. We also suggest a continuous-time version of Viterbi algorithm for this Markov double chain model, which is viable for obtaining the MAP estimation of the set of locations of changepoints. The model formulation and the continuous-time version of forward-filtering backward-sampling algorithm and Viterbi algorithm can be extended to simultaneously monitor the structural breaks of multiple Markov jump processes, which may have either variable transition rate matrix or identical transition rate matrix. We then perform a numerical study to demonstrate the methods. In numerical examples, we compare the performance of the FFBS algorithm via inverse transformation with the FFBS algorithm via uniformization. The two algorithms performs well in different cases. These models are potentially viable for modelling the credit rating dynamics in credit risk management.