Markov Chain Monte Carlo methods for discretely observed continuous-time semi-Markov models

Inference for continuous time multi-state models presents considerable computational difficulties when the process is only observed at discrete time points with no additional information about the state transitions. In particular, when transitions between states may depend on the time since entry into the current state, and semi-Markov models should be fitted to the data, the likelihood function is neither available in closed form. In this paper we propose a Markov Chain Monte Carlo algorithm to simulate the posterior distribution of the model parameters.