Parameter estimation via stochastic variants of the ECM algorithm with applications to plant growth modeling

Mathematical modeling of plant growth has gained increasing interest in recent years due to its potential applications. A general family of models, known as functional–structural plant models (FSPMs) and formalized as dynamic systems, serves as the basis for the current study. Modeling, parameterization and estimation are very challenging problems due to the complicated mechanisms involved in plant evolution. A specific type of a non-homogeneous hidden Markov model has been proposed as an extension of the GreenLab FSPM to study a certain class of plants with known organogenesis. In such a model, the maximum likelihood estimator cannot be derived explicitly. Thus, a stochastic version of an expectation conditional maximization (ECM) algorithm was adopted, where the E-step was approximated by sequential importance sampling with resampling (SISR). The complexity of the E-step creates the need for the design and the comparison of different simulation methods for its approximation. In this direction, three variants of SISR and a Markov Chain Monte Carlo (MCMC) approach are compared for their efficiency in parameter estimation on simulated and real sugar beet data, where observations are taken by censoring plant’s evolution (destructive measurements). The MCMC approach seems to be more efficient for this particular application context and also for a large variety of crop plants. Moreover, a data-driven automated MCMC–ECM algorithm for finding an appropriate sample size in each ECM step and also an appropriate number of ECM steps is proposed. Based on the available real dataset, some competing models are compared via model selection techniques.