Bayesian spatial prediction of the site index in the study of the Missouri Ozark Forest Ecosystem Project

This paper presents a Bayesian spatial method for analysing the site index data from the Missouri Ozark Forest Ecosystem Project (MOFEP). Based on ecological background and availability, we select three variables, the aspect class, the soil depth and the land type association as covariates for analysis. To allow great flexibility of the smoothness of the random field, we choose the Matérn family as the correlation function. We adopt the reference prior as an appropriate prior because there is no previous knowledge of the parameters in the model. An efficient algorithm based on the generalized Ratio-of-Uniforms method is developed for the posterior simulation. One advantage of the algorithm is that it generates independent samples from the required posterior distribution, which is much more efficient for both statistical inference of the parameters and prediction of the site indexes at unsampled locations. Our results show that the aspect class and the soil depth are both significant while the land type association is less significant. The model validation is briefly discussed. In addition, our simulation method allows easy realization for computing quantities from the posterior predictive distributions.