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Abstract: Hidden Markov models (HMMs) can infer biological rhythms by linking observations to underlying latent states of the biological process, often assuming state transition probabilities follow fixed, regular cycles. However, rhythms can fluctuate due to internal and external factors. I extend HMMs to model “irregular rhythms” that vary in frequency or stability over time. I analyze motor activity data from patients with depression to infer their circadian rhythms, which repeat every 24 hours but often exhibit irregularities. To jointly model state transition probabilities across all patients, accounting for daily behavioural cycles, daily variability, and individual variability, I formulate these probabilities to depend on time-of-day, day, and random effects. This approach provides insights into the regularities and trends of state-switching dynamics, revealing that transition probabilities do not always adhere to a regular daily cycle. Overall, this work advances the modelling of irregular rhythms in HMMs and contributes to a deeper understanding of circadian-related health issues.