Environmental conditions in semi-enclosed basins: A dynamic latent class approach for mixed-type multivariate variables

Bulla, Jan; Lagona, Francesco; Maruotti, Antonello; Picone, Marco

Journal de la société française de statistique, Tome 156 (2015) no. 1, pp. 114-137.

L’identification des conditions environnementales typiques basée sur plusieurs séries chronologiques d’observations linéaires et circulaires nécessite des méthodes de classification qui tiennent compte des dépendances aussi bien temporelles que dans l’ensemble des variables. Motivé par une étude de cas centré autour de caractéristiques marines, nous adoptons une analyse de structure latente comme classification, en s’appuyant sur un modèle de Markov caché multivarié. Le modèle intègre des densités multivariées von Mises et log-normales pour décrire la distribution que la vitesse du vent et la hauteur des vagues ainsi que la direction du vent et des vagues prennent sous différents régimes latents, avec des paramètres qui dépendent de l’évolution d’une chaîne de Markov non observée. L’estimation du modèle est facilitée par un algorithme hybride qui combine un algorithme EM avec maximisation directe de la log-vraisemblance.

Notre analyse des données marines de deux régions de la Méditerranée montre qu’une approche de Markov caché comme classification peut être utilisée avec succès pour identifier les conditions marines interprétables dans les milieux orographiques complexes.

The identification of typical environmental conditions from multiple time series of linear and circular observations requires classification methods that account for the dependence across variables and in time. Motivated by a case study of sea conditions, we take a latent-class approach to classification, relying on a multivariate hidden Markov model. The model integrates multivariate von Mises and log-normal densities to describe the distribution that wind speed and wave height as well as wind and wave direction take under different latent regimes, with parameters that depend on the evolution of an unobserved Markov chain. The estimation of the model is facilitated by a hybrid algorithm that combines an EM algorithm with direct maximization of the log-likelihood.

Our analysis of marine data from two locations in the Mediterranean shows that a hidden Markov approach to classification can be successfully employed for identifying interpretable marine conditions in complex orographic settings.

Mots clés : Circular data, EM algorithm, Hidden Markov model, Model-based clustering, Skewness, Unsupervised classification, Wave, Wind

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