Simulation techniques for parameter estimation via a stochastic 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 of Carbon allocation formalized as dynamic systems serves as the basis for our study. They are known as functional-structural plant models (FSPMs, [45]). Modeling, parameterization and estimation are very challenging problems due to the complicated mechanisms involved in plant evolution. In [46] a specific type of a non-homogeneous hidden Markov model is proposed as an extension of the GreenLab FSPM ([9]) to study a certain class of plants with known organogenesis. In such a model, the maximum likelihood estimator cannot be derived explicitly. A stochastic version of an ECM (expectation conditional maximization) algorithm was adopted, where the E-step was approximated by a sequential importance sampling with resampling method (SISR-ECM approach). In this paper, a Markov Chain Monte Carlo method is proposed for the approximation of the E-step (MCMC-ECM approach). The parameter estimates obtained with MCMC-ECM are compared with those obtained with SISR-ECM from simulated and real sugar beet data. Based on this real data set competing models are compared via model selection techniques. Moreover, a data-driven automated MCMC-ECM algorithm for finding the proper sample size in each ECM step and also the proper number of ECM steps is proposed. The MCMC approach seems to be more flexible for this particular application context and can be more easily generalized to the parameter estimation of other plant models for which observations are taken under destructive measurements. keywords: plant growth model; hidden Markov model; stochastic ECM algorithm; MCMC; Metropolis-within-Gibbs; automated Monte-Carlo EM algorithm; sequential importance sampling with resampling