A Bayesian approach to crop model calibration under unknown error covariance.

摘要

Bayesian methods seem well adapted to dynamic system models in general and to crop models in particular, because there is in general prior information about parameter values. The usefulness of a Bayesian approach has often been pointed out, but actual applications are rather rare. A major difficulty is including the elements of the covariance matrix of model errors in the treatment. We treat the specific case of balanced data and an unstructured covariance matrix. In our particular case this is a 3x3 matrix. We illustrate two methods for deriving a sample from the joint posterior density for the crop model parameters and the error covariance matrix parameters. The first method is based on importance sampling, the second on Metropolis within Gibbs sampling. We derive an instrumental density for the former and a proposal density for the latter which are adapted to this type of model and data. Both algorithms work well and they give very similar results. The example concerns a model for sunflowers during rapid leaf growth. The ultimate goal is to use the model as a decision aid in predicting disease risk.