Continuous-Time Hidden Markov Models

Continuous-Time Hidden Markov Models (CT-HMMs) are statistical tools used to analyze systems that change over time in ways that aren’t directly observable. They assume the system moves between different states randomly, with the timing of these changes following a continuous clock. While we can't see the states directly, we observe related data (like signals or outputs). CT-HMMs help us infer the hidden states' sequence and transition rates, providing insights into the underlying process's dynamics. They are useful in areas like biology, finance, and engineering, where systems evolve continuously and are only partially observable.