Bayesian inference for discretely observed non-homogeneous Markov processes

Inference for continuous time non homogeneous multi-state Markovmodels may present considerable computational difficulties when the process isonly observed at discrete time points without additional information about the statetransitions. In fact, the likelihood can be obtained numerically only by solving theChapman-Kolmogorov equations satisfied by the model transition probabilities. Inthis paper we propose to make Bayesian inference bypassing the likelihood calcula-tion by simulating the whole continuous trajectories conditionally on the observedpoints via a Metropolis-Hastings step based on a piecewise homogeneous Markovprocess. A benchmark data set in the multi-state model literature is used to illustratethe resulting inference.