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Hidden semi-Markov Models (HSMM's) - while broadly in use - are restricted toa discrete and uniform time grid. They are thus not well suited to explainoften irregularly spaced discrete event data from continuous-time phenomena. Weshow that non-sampling-based latent state inference used in HSMM's can begeneralized to latent Continuous-Time semi-Markov Chains (CTSMC's). Weformulate integro-differential forward and backward equations adjusted to theobservation likelihood and introduce an exact integral equation for theBayesian posterior marginals and a scalable Viterbi-type algorithm forposterior path estimates. The presented equations can be efficiently solvedusing well-known numerical methods. As a practical tool, variable-step HSMM'sare introduced. We evaluate our approaches in latent state inference scenariosin comparison to classical HSMM's.

Forward-Backward Latent State Inference for Hidden Continuous-Time semi-Markov Chains