Non-parametric Observation Driven HMM - INRAE - Institut national de recherche pour l’agriculture, l’alimentation et l’environnement Access content directly
Preprints, Working Papers, ... (Preprint) Year :

Non-parametric Observation Driven HMM

HMM non paramétrique piloté par les observations


The hidden Markov models (HMM) are used in many different fields, to study the dynamics of a process that cannot be directly observed. However, in some cases, the structure of dependencies of a HMM is too simple to describe the dynamics of the hidden process. In particular, in some applications in finance or in ecology, the transition probabilities of the hidden Markov chain can also depend on the current observation. In this work we are interested in extending the classical HMM to this situation. We define a new model, referred to as the Observation Driven-Hidden Markov Model (OD-HMM). We present a complete study of the general non-parametric OD-HMM with discrete and finite state spaces (hidden and observed variables). We study its identifiability. Then we study the consistency of the maximum likelihood estimators. We derive the associated forward-backward equations for the E-step of the EM algorithm. The quality of the procedure is tested on simulated data sets. Finally, we illustrate the use of the model on an application on the study of annual plants dynamics. This works sets theoretical and practical foundations for a new framework that could be further extended, on one hand to the non-parametric context to simplify estimation, and on the other hand to the hidden semi-Markov models for more realism.
Fichier principal
Vignette du fichier
Preprint_article_OD_HMM.pdf (402.39 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-04053732 , version 1 (02-06-2023)


  • HAL Id : hal-04053732 , version 1


Hanna Bacave, Pierre-Olivier Cheptou, Nikolaos Limnios, Nathalie Peyrard. Non-parametric Observation Driven HMM. 2023. ⟨hal-04053732⟩
40 View
13 Download


Gmail Facebook Twitter LinkedIn More