The inclusion of covariates in models for analysing variety by environmental data sets allows the estimation of variety yields for specific locations within a region as well as for the region as a whole. Here we explore a Bayesian approach to the estimation of such effects, and to the choice of variety, using a possibly incomplete variety by location by year data set which includes location by year covariates. This approach allows expert knowledge of the crop and uncertainty about local circumstances to be incorporated in the analysis. It is implemented using Markov chain Monte Carlo simulation. An example is used to illustrate the approach and investigate its robustness.