Extension of Hidden (semi-)Markov Models to estimate weed dynamics
Hanna Bacave
In agriculture, understanding weed dynamics plays a key role in the study of ecosystems. However it is not possible to observe populations at all stages of their dynamics, as some stages are hidden. Hidden Markov Models (HMM) are effective for modeling their dynamics, but the assumptions of conditional independence can be too strong. Indeed, they do not account for the interactions between the hidden sub-population (part of the population in an unobservable life stage) and the observed sub-population. This is why we introduce Observation-Driven Hidden Markov Models (OD-HMM) to model the influence of the standing flora (grown plants) on the state of the hidden seed bank. In the non-parametric framework, we propose a theoretical study of the model: analysis of its identifiability and the consistency of its maximum likelihood estimator. From an operational perspective, we develop the associated EM algorithm. Finally, we illustrate the relevance of the OD-HMM by studying the dynamics of non-dormant weed species. We then discuss the limitations specific to the OD-HMM. Seed dormancy, which can last several years, makes the OD-HMM (where the probability of changing state does not depend on the time spent in the current state) unsuitable. Drawing inspiration from Hidden Semi-Markov Models (HSMM), we therefore propose the OD-HSMM. Theoretically, we discuss its formalization and present a parameterization of this model based on key parameters of weed dynamics. Algorithmically, we explore two estimation approaches: the EM algorithm and the ABC algorithm. This work thus extends the framework of HMMs in two ways: first, by introducing the OD-HMM to more realistically model the dynamics of weeds; and also, by developing the OD-HSMM to account for the duration during which seeds remain in the seed bank.