Bayesian estimation of the parameters of a nonlinear model. An application to human height

The estimation of the parameters of a nonlinear model by means of the maximum likelihood procedure is widely used in the study of growth phenomena. The accuracy with which these parameters are calculated is a function of the number of measures taken and particularly, of their distribution across the growth period. If the growth curve is only partially known, the inaccuracy can increase considerably. However, if we have information on the distribution of the parameters of a model in the population, the empirical Bayes method should be used. In this paper, the principle of this approach for nonlinear modeling was recalled. The method was then applied on data of human height. Four nonlinear models are used and their performances are compared. The results show the importance of information on the quality of estimates of growth parameters and consequently on the prediction of adult height.