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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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 / KeywordsMixed models; Growth curves; Gompertz model; Euler-Maruyama scheme; Bayesian estimation;; Stochastic differential equation; Predictive posterior distribution
Showing items related by title and author.
EM algorithm coupled with particle filter for maximum likelihood parameter estimation of stochastic differential mixed-effects models Samson, Adeline; Donnet, Sophie (2010) Document de travail / Working paper
Analyse bayésienne de courbes de croissance par des modèles à effets mixtes définis par équations différentielles stochastiques. Donnet, Sophie; Foulley, Jean-Louis; Samson, Adeline (2009) Communication / Conférence