Approximate bayesian Inference for discretely observed continuous- time multi-state models

Inferenceforcontinuoustimemulti-statemodelspresentsconsiderablecomputationaldif- ficulties when the process is only observed at discrete time points with no additional information about the state transitions. In fact, for general multi-state Markov model, the evaluation of the likelihood func- tion is possible only via intensive numerical approximations. Moreover, in real applications, transitions between states may depend on the time since entry into the current state and semi-Markov models, where the likelihood function is not available in closed form, should be fitted to the data. Approxi- mate Bayesian Computation (ABC) methods, which make use only of comparisons between simulated and observed summary statistics, represent a solution to intractable likelihood problems and provide alternative algorithms when the likelihood calculation is computationally too costly. In this paper we investigate the potentiality of ABC techniques for multi-state models by means of a real data example.