A sequential Monte Carlo approach for MLE in a plant growth model

Samis Trevezas 1 Paul-Henry Cournède 1, 2
1 DIGIPLANTE - Modélisation de la croissance et de l'architecture des plantes
MAS - Mathématiques Appliquées aux Systèmes - EA 4037, CIRAD - Centre de Coopération Internationale en Recherche Agronomique pour le Développement, Inria Saclay - Ile de France, Ecole Centrale Paris
Abstract : Parametric identification of plant growth models formalized as discrete dynamical systems is a challenging problem due to specific data acquisition (system observation is generally done with destructive measurements), non-linear dynamics, model uncertainties and high-dimensional parameter space. In this study, we present a novel idea of modeling plant growth in the framework of non-homogeneous hidden Markov models (Cappé et al., 2005), for a certain class of plants with known organogenesis (structural development). Unknown parameters of the models are estimated via a stochastic variant of a generalised EM (Expectation-Maximization) algorithm and approximate confidence intervals are given via parametric bootstrap. The complexity of the model makes both the E-step and the M-step non-explicit. For this reason, the E-step is approximated via a sequential Monte-Carlo procedure (sequential importance sampling with resampling) and the M-step is separated into two steps (Conditional-Maximization), where before applying a numerical maximization procedure (quasi-Newton type), a large subset of unknown parameters is updated explicitly conditioned on the other subset. A simulation study and a case-study with real data from the sugar-beet are considered and a model comparison is performed based on these data. Appendices are available online.
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Submitted on : Friday, March 1, 2013 - 5:06:35 PM
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Samis Trevezas, Paul-Henry Cournède. A sequential Monte Carlo approach for MLE in a plant growth model. Journal of Agricultural, Biological, and Environmental Statistics, Springer Verlag, 2013, pp.online first. ⟨10.1007/s13253-013-0134-1⟩. ⟨hal-00796154⟩



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