Charlotte Baey (Ecole Centrale Paris): stochastic algorithms for nonlinear mixed models

There is a strong genetic variability among plants, even of the same variety, which, combined with the locally varying climatic effects in a given field, can lead to the development of highly different neighbouring plants. This is one of the reasons why population-based methods for modelling plant growth are of great interest. The functional structural plant growth model, called GreenLab, has already been shown to be successful in describing plant growth dynamics primarily in an 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 nonlinear 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 where 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 automated 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.

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