MCMC inference for semi Markov models
Semi-Markov processes are stochastic processes widely used to model many phenomena in finance, as well as in different disciplines. However, several improvements might be made in the Bayesian computational inference framework. The goal of this work is to provide a Markov chain Monte Carlo method for estimating parameters of multi state processeses, extending some estimators already provided in literature for Markov jump Processes, to the more general case of semi-Markov processes. Specifically, for discrete observation of continuous time processes, our algorithm will be able to simulate the trajectories between the observed point and estimate the parameters governing the process. This by a two-phase algorithm: in the first step the parameters generating the process are simulated, while in the second phase these are used for the rate matrix generation, which is input the function that simulates semi-Markov paths and provide information for the next iteration.