Flexible estimation of the state dwell-time distribution in hidden semi-Markov models

J. Pohle*, T. Adam, L.T. Beumer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Hidden semi-Markov models generalise hidden Markov models by explicitly modelling the time spent in a given state, the so-called dwell time, using some distribution defined on the natural numbers. While the (shifted) Poisson and negative binomial distribution provide natural choices for such distributions, in practice, parametric distributions can lack the flexibility to adequately model the dwell times. To overcome this problem, a penalised maximum likelihood approach is proposed that allows for a flexible and data-driven estimation of the dwell-time distributions without the need to make any distributional assumption. This approach is suitable for direct modelling purposes or as an exploratory tool to investigate the latent state dynamics. The feasibility and potential of the suggested approach is illustrated in a simulation study and by modelling muskox movements in northeast Greenland using GPS tracking data. The proposed method is implemented in the R-package PHSMM which is available on CRAN.
Original languageEnglish
Article number107479
Number of pages15
JournalComputational Statistics and Data Analysis
Early online date31 Mar 2022
Publication statusPublished - 1 Aug 2022


  • Animal movement modeling
  • Penalized likelihood
  • Smoothing
  • Time series


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