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 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, Moulines, and Rydén 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 generalized EM (Expectation-Maximization) algorithm and approximate confidence intervals are given via parametric bootstrap. The complexity of the model makes both the E-step (expectation step) and the M-step (maximization 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.