A Regularized Particle Filter EM Algorithm Based on Gaussian Randomization with an Application to Plant Growth Modeling

Yuting Chen, Samis Trevezas () and Paul-Henry Cournède
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Yuting Chen: Laboratoire de Mathématiques Appliquées aux Systèmes
Samis Trevezas: Laboratoire de Mathématiques Appliquées aux Systèmes
Paul-Henry Cournède: Laboratoire de Mathématiques Appliquées aux Systèmes

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 4, 847-870

Abstract: Abstract Parameter estimation in complex models arising in real data applications is a topic which still attracts a lot of interest. In this article, we study a specific data and parameter augmentation method which gives us the opportunity to estimate more easily the parameters of the initial model. For this reason, the notion of Gaussian randomization of a model with respect to some of its parameters is introduced. The initial model can be regarded as a submodel of the resulting extended incomplete data model. Under the assumption that the initial model has a unique maximum likelihood estimator (MLE) and that the likelihood function is continuous we prove that the extended model has a unique MLE with common values for the parameters of the MLE which correspond to the initial model. We also prove the reverse direction. Moreover, an appropriate stochastic version of an EM (Expectation-Maximization) algorithm is suggested to make parameter estimation feasible. In particular, we describe how the regularized particle filter of Musso and Oudjane (1998) can be used in this frequentist-based approach to perform the Monte Carlo E-step at each iteration of the stochastic EM algorithm. This regularized version is particularly adapted to the framework of Gaussian randomization since the last iterations of the EM algorithm are characterized by low variance in the parameter distributions. A toy example with available analytic solutions, a synthetic example and a real data application with scarce observations to the LNAS (Log-Normal Allocation and Senescence) model of sugar beet growth are presented to highlight some theoretical and practical aspects of the proposed methodology.

Keywords: Gaussian randomization; Stochastic EM algorithm; Regularized particle filter; Plant growth model; LNAS model; State space model; 60K10; 62F99; 62P10 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-015-9440-0

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