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Bayesian analysis of growth curves using mixed models defined by stochastic differential equations
- Source :
- Biometrics, Biometrics, Wiley, 2010, 66 (3), pp.733-741. 〈10.1111/j.1541-0420.2009.01342.x〉, Biometrics, Wiley, 2010, 66 (3), pp.733-741. ⟨10.1111/j.1541-0420.2009.01342.x⟩
- Publication Year :
- 2009
-
Abstract
- International audience; Growth curve data consist of repeated measurements of a continuous growth process over time among 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 diusion 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 chichen growth, the modeling being improved by the SDE approach.
- Subjects :
- Statistics and Probability
Mixed model
Predictive posterior distribution
Mathematical optimization
Gompertz function
Posterior probability
Population
Growth
Bayesian inference
Growth curves
01 natural sciences
Growth curve (statistics)
General Biochemistry, Genetics and Molecular Biology
Euler-Maruyama scheme
010104 statistics & probability
03 medical and health sciences
Stochastic differential equation
Applied mathematics
Animals
Humans
0101 mathematics
Mixed models
education
030304 developmental biology
Mathematics
0303 health sciences
education.field_of_study
[STAT.AP]Statistics [stat]/Applications [stat.AP]
General Immunology and Microbiology
Applied Mathematics
[ STAT.AP ] Statistics [stat]/Applications [stat.AP]
Gompertz model
Bayes Theorem
General Medicine
Conditional probability distribution
Bayesian estimation
Models, Theoretical
[ STAT.ME ] Statistics [stat]/Methodology [stat.ME]
General Agricultural and Biological Sciences
[STAT.ME]Statistics [stat]/Methodology [stat.ME]
Chickens
Algorithms
Subjects
Details
- ISSN :
- 15410420 and 0006341X
- Volume :
- 66
- Issue :
- 3
- Database :
- OpenAIRE
- Journal :
- Biometrics
- Accession number :
- edsair.doi.dedup.....9c7c954cd32325e2bd6ed8ee6c518156