Samis Trevezas

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.

A non linear mixed effects model of plant growth and estimation via stochastic variants of the EM algorithm

ABSTRACT There is a strong genetic variability among plants, even of the same variety, which, combined with the locally varying environmental conditions in a given field, can lead to the development of highly different neighboring plants. This is one of the reasons why population-based methods for modeling plant growth are of great interest. GreenLab is a functional–structural plant growth model which has already been shown to be successful in describing plant growth dynamics primarily at individual level. In this study, we extend its formulation to the population level. In order to model the deviations from some fixed but unknown important biophysical and genetic parameters we introduce random effects. The resulting model can be cast into the framework of non linear mixed models, which can be seen as particular types of incomplete data models. A stochastic variant of an EM-type algorithm (expectation–maximization) is generally needed to perform maximum likelihood estimation for this type of models. Under some assumptions, the complete data distribution belongs to a subclass of the exponential family of distributions for which the M-step can be solved explicitly. In such cases, the interest is focused on the best approximation of the E-step by competing simulation methods. In this direction, we propose to compare two commonly used stochastic algorithms: the Monte-Carlo EM (MCEM) and the SAEM algorithm. The performances of both algorithms are compared on simulated data, and an application to real data from sugar beet plants is also given.

Exact MLE and asymptotic properties for nonparametric semi-Markov models

This article concerns maximum-likelihood estimation for discrete time homogeneous nonparametric semi-Markov models with finite state space. In particular, we present the exact maximum-likelihood estimator of the semi-Markov kernel which governs the evolution of the semi-Markov chain (SMC). We study its asymptotic properties in the following cases: (i) for one observed trajectory, when the length of the observation tends to infinity, and (ii) for parallel observations of independent copies of an SMC censored at a fixed time, when the number of copies tends to infinity. In both cases, we obtain strong consistency, asymptotic normality, and asymptotic efficiency for every finite dimensional vector of this estimator. Finally, we obtain explicit forms for the covariance matrices of the asymptotic distributions.