The article by Bez et al [1] addresses an important issue for statisticians and ecological modellers: the impact of modelling choices when considering state-space models to represent time series with hidden regimes.

The authors present an empirical study of the impact of model misspecification for models in the HMM and HSMM family. The misspecification can be at the level of the hidden chain (Markovian or semi-Markovian assumption) or at the level of the observed chain (AR0 or AR1 assumption). 

The study uses data on the movements of fishing vessels. Vessels can exert pressure on fish stocks when they are fishing, and the aim is to identify the periods during which fishing vessels are fishing or not fishing, based on GPS tracking data. Two sets of data are available, from two vessels with contrasting fishing behaviour. The empirical study combines experiments on the two real datasets and on data simulated from models whose parameters are estimated on the real datasets. In both cases, the actual sequence of activities is available. The impact of a model misspecification is mainly evaluated on the restored hidden chain (decoding task), which is very relevant since in many applications we are more interested in the quality of decoding than in the accuracy of parameters estimation. Results on parameter estimation are also presented and metrics are developed to help interpret the results. The study is conducted in a rigorous manner and extensive experiments are carried out, making the results robust.

The main conclusion of the study is that choosing the wrong AR model at the observed sequence level has more impact than choosing the wrong model at the hidden chain level.

The article ends with an interesting discussion of this finding, in particular the impact of resolution on the quality of the decoding results. As the authors point out in this discussion, the results of this study are not limited to the application of GPS data to the activities of fishing vessels Beyond ecology, H(S)MMs are also widely used epidemiology, seismology, speech recognition, human activity recognition ... The conclusion of this study will therefore be useful in a wide range of applications. It is a warning that should encourage modellers to design their hidden Markov models carefully or to interpret their results cautiously.

References

[1] Nicolas Bez, Pierre Gloaguen, Marie-Pierre Etienne, Rocio Joo, Sophie Lanco, Etienne Rivot, Emily Walker, Mathieu Woillez, Stéphanie Mahévas (2024) Proper account of auto-correlations improves decoding performances of state-space (semi) Markov models. HAL, ver.3 peer-reviewed and recommended by PCI Math Comp Biol https://hal.science/hal-04547315v3