A novel method and comparison of methods for constructing Markov bridges
In this work, we consider the problem of statistical inference for Markov jump processes based on discrete time observations. We review some methods to generate sample paths from a Markov jump process conditioned to endpoints (Markov bridges), and present a new algorithm based on the idea of time-reversed. We use the proposed method to estimate the infinitesimal generator of a Markov jump process via a Markov Chain Monte Carlo method and the Monte Carlo Expectation-Maximization algorithm, obtaining good estimates of the parameters. Moreover, we provide a comparative analysis of the methods in terms of their speed and accuracy, being the proposed method the faster one.
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