Using a Bayesian approach to parameter estimation; comparison of the GLUE and MCMC methods

The Bayesian approach allows one to estimate model parameters from prior expert knowledge about parameter values and from experimental data. The purpose of this paper is to compare the performances of two Bayesian methods, namely the Metropolis-Hastings algorithm and the Generalized Likelihood Uncertainty Estimation method (GLUE). These two methods are applied to a non-linear model that includes 22 parameters. This model has the main features of an agronomic model. The two Bayesian methods give similar results. The parameter estimates obtained with the two methods have similar properties. Both methods improve strongly the accuracy of model predictions even when only few data samples are available for estimating the parameters. However, the values of mean squared error of prediction of the model are slightly higher with the GLUE method than with the Metropolis-Hastings algorithm. The performances of the methods are sensitive to the prior assumptions made about parameter values.