A novel method and comparison of methods for constructing Markov bridges
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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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