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Bayesian analysis of growth curves using mixed models defined by stochastic differential equations

Foulley, Jean-Louis; Samson, Adeline; Donnet, Sophie (2010), Bayesian analysis of growth curves using mixed models defined by stochastic differential equations, Biometrics, 66, 3, p. 733-741. http://dx.doi.org/10.1111/j.1541-0420.2009.01342.x

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Type
Article accepté pour publication ou publié
Date
2010
Journal name
Biometrics
Volume
66
Number
3
Publisher
International Biometric Society
Pages
733-741
Publication identifier
http://dx.doi.org/10.1111/j.1541-0420.2009.01342.x
Metadata
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Author(s)
Foulley, Jean-Louis
Samson, Adeline
Donnet, Sophie cc
Abstract (EN)
Growth curve data consist of repeated measurements of a continuous growth process over time in a population of individuals. These data are classically analyzed by nonlinear mixed models. However, the standard growth functions used in this context prescribe monotone increasing growth and can fail to model unexpected changes in growth rates. We propose to model these variations using stochastic differential equations (SDEs) that are deduced from the standard deterministic growth function by adding random variations to the growth dynamics. A Bayesian inference of the parameters of these SDE mixed models is developed. In the case when the SDE has an explicit solution, we describe an easily implemented Gibbs algorithm. When the conditional distribution of the diffusion process has no explicit form, we propose to approximate it using the Euler-Maruyama scheme. Finally, we suggest to validate the SDE approach via criteria based on the predictive posterior distribution. We illustrate the efficiency of our method using the Gompertz function to model data on chicken growth, the modeling being improved by the SDE approach.
Subjects / Keywords
Mixed models; Growth curves; Gompertz model; Euler-Maruyama scheme; Bayesian estimation;; Stochastic differential equation; Predictive posterior distribution
JEL
C11 - Bayesian Analysis: General

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