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

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 highdimensional parameter space. In this study, we present a novel idea of modeling plant growth in the framework of non-homogeneous hidden Markov models ([6]), 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. keywords: dynamical system; ECM algorithm; maximum likelihood estimation; parametric identification; plant growth model; sequential Monte-Carlo