Section: Mathematical & Computational Biology
Topic: Ecology, Statistics

Proper account of auto-correlations improves decoding performances of state-space (semi) Markov models

Bez, Nicolas1  ; Gloaguen, Pierre2 ; Etienne, Marie-Pierre3 ; Lanco, Sophie1 ; Joo, Rocío4 ; Rivot, Etienne5 ; Walker, Emily6; Woillez, Mathieu5 ; Mahévas, Stéphanie1 
1 MARBEC, Université de Montpellier, IRD, CNRS, Ifremer, Sète, France
2 Université Bretagne Sud, UMR CNRS 6205, LMBA, F-56000 Vannes, France
3 Institut de Recherche Mathématique de Rennes, Rennes, France
4 Global Fishing Watch
5 DECOD (Dynamique et Durabilité des Ecosystèmes), L'Institut Agro, INRAE, Ifremer, Rennes, France
6 INRAE, BioSP, 84914, Avignon, France

Corresponding author(s): Bez, Nicolas (nicolas.bez@ird.fr)

10.24072/pcjournal.535 - Peer Community Journal, Volume 5 (2025), article no. e38.

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State-space models are widely used in ecology to infer hidden behaviors. This study develops an extensive numerical simulation-estimation experiment to evaluate the state decoding accuracy of four simple state-space models. These models are obtained by combining different Markovian specifications (Markov and semi-Markov) for the hidden layer with the absence (model AR0) and presence (AR1) of auto-correlation for the observation layer. Model parameters are issued from two sets of real annotated trajectories. Three metrics are developed to help interpret model performance. The first is the Hellinger distance between Markov and semi-Markov sojourn time probability distributions. The second is sensitive to the overlap between the probability density functions of state-dependent variables (e.g., speed variables). The third quantifies the deterioration of the inference conditions between AR0 and AR1 formulations. It emerges that the most sensitive model choice concerns the auto-correlation of the random processes describing the state-dependent variables. Opting for the absence of auto-correlation in the model while the state-dependent variables are actually auto-correlated, is detrimental to state decoding performance. Regarding the hidden layer, imposing a Markov structure while the state process is semi-Markov (with negative Binomial sojourn times) does not impair the state decoding performances. The real-life estimates are consistent with our experimental finding that performance deteriorates when there are significant temporal correlations that are not accounted for in the model. In light of these findings, we recommend that researchers carefully consider the structure of the statistical model they suggest and confirm its alignment with the process being modeled, especially when considering the auto-correlation of observed variables.

Published online:
DOI: 10.24072/pcjournal.535
Type: Research article
Keywords: Hidden Markov models, Hidden semi-Markov models, State decoding accuracy, Simulationestimation, Auto-regressive process, Ground truth, Hidden Markov models, Hidden semi-Markov models, State decoding accuracy, Simulationestimation, Auto-regressive process, Ground truth, Hidden Markov models, Hidden semi-Markov models, State decoding accuracy, Simulationestimation, Auto-regressive process, Ground truth, Hidden Markov models, Hidden semi-Markov models, State decoding accuracy, Simulationestimation, Auto-regressive process, Ground truth

Bez, Nicolas 1; Gloaguen, Pierre 2; Etienne, Marie-Pierre 3; Lanco, Sophie 1; Joo, Rocío 4; Rivot, Etienne 5; Walker, Emily 6; Woillez, Mathieu 5; Mahévas, Stéphanie 1

1 MARBEC, Université de Montpellier, IRD, CNRS, Ifremer, Sète, France
2 Université Bretagne Sud, UMR CNRS 6205, LMBA, F-56000 Vannes, France
3 Institut de Recherche Mathématique de Rennes, Rennes, France
4 Global Fishing Watch
5 DECOD (Dynamique et Durabilité des Ecosystèmes), L'Institut Agro, INRAE, Ifremer, Rennes, France
6 INRAE, BioSP, 84914, Avignon, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {Proper account of auto-correlations improves decoding performances of state-space (semi) {Markov} models},
     journal = {Peer Community Journal},
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Bez, Nicolas; Gloaguen, Pierre; Etienne, Marie-Pierre; Lanco, Sophie; Joo, Rocío; Rivot, Etienne; Walker, Emily; Woillez, Mathieu; Mahévas, Stéphanie. Proper account of auto-correlations improves decoding performances of state-space (semi) Markov models. Peer Community Journal, Volume 5 (2025), article  no. e38. doi : 10.24072/pcjournal.535. https://peercommunityjournal.org/articles/10.24072/pcjournal.535/

PCI peer reviews and recommendation, and links to data, scripts, code and supplementary information: 10.24072/pci.mcb.100316

Conflict of interest of the recommender and peer reviewers:
The recommender in charge of the evaluation of the article and the reviewers declared that they have no conflict of interest (as defined in the code of conduct of PCI) with the authors or with the content of the article.

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