Time-coherency of Bayesian priors on transient semi-Markov chains for audio-to-score alignment

This paper proposes a novel insight to the problem of real-time alignment with Bayesian inference. When a prior knowledge about the duration of events is available, Semi-Markov models allow the setting of individual duration distributions but give no clue about their choice. We propose a criterion of temporal coherency for such applications and show it might be obtained with the right choice of estimation method. Theoretical insights are obtained through the study of the prior state probability of transient semi-Markov chains.