Maximum likelihood trajectories for continuous-time Markov chains

摘要: Continuous-time Markov chains are used to model systems in which transitions between states as well the time system spends each state random. Many computational problems related such have been solved, including determining distributions a function of time, parameter estimation, and control. However, problem inferring most likely trajectories, where trajectory is sequence amount spent state, appears unsolved. We study three versions this problem: (i) an initial value problem, given we seek until final (ii) boundary times given, connecting them, (iii) inference under partial observability, analogous finding maximum likelihood trajectories for hidden models. show that not always well-defined, describe polynomial test well-definedness. When well-definedness holds, can be solved develop efficient dynamic programming algorithms doing so.