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

Author

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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)

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.

Suggested Citation

  • Yuting Chen & Samis Trevezas & Paul-Henry Cournède, 2015. "A Regularized Particle Filter EM Algorithm Based on Gaussian Randomization with an Application to Plant Growth Modeling," Methodology and Computing in Applied Probability, Springer, vol. 17(4), pages 847-870, December.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:4:d:10.1007_s11009-015-9440-0
    DOI: 10.1007/s11009-015-9440-0
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    References listed on IDEAS

    as
    1. Trevezas, S. & Malefaki, S. & Cournède, P.-H., 2014. "Parameter estimation via stochastic variants of the ECM algorithm with applications to plant growth modeling," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 82-99.
    2. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    3. Chen, Yuting & Cournède, Paul-Henry, 2014. "Data assimilation to reduce uncertainty of crop model prediction with Convolution Particle Filtering," Ecological Modelling, Elsevier, vol. 290(C), pages 165-177.
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    1. D. Logothetis & S. Malefaki & S. Trevezas & P.-H. Cournède, 2022. "Bayesian Estimation for the GreenLab Plant Growth Model with Deterministic Organogenesis," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(1), pages 63-87, March.

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