A Bayesian Approach to Estimating Seemingly Unrelated Regression for Tree Biomass Model Systems

Abstract

Accurate estimation of tree biomass is required for accounting for and monitoring forest carbon stocking. Allometric biomass equations constructed by classical statistical methods are widely used to predict tree biomass in forest ecosystems. In this study, a Bayesian approach was proposed and applied to develop two additive biomass model systems: one with tree diameter at breast height as the only predictor and the other with both tree diameter and total height as the predictors for planted Korean larch (Larix olgensis Henry) in the Northeast, P.R. China. The seemingly unrelated regression (SUR) was used to fit the simultaneous equations of four tree components (i.e., stem, branch, foliage, and root). The model parameters were estimated by feasible generalized least squares (FGLS) and Bayesian methods using either non-informative priors or informative priors. The results showed that adding tree height to the model systems improved the model fitting and performance for the stem, branch, and foliage biomass models, but much less for the root biomass models. The Bayesian methods on the SUR models produced narrower 95% prediction intervals than did the classical FGLS method, indicating higher computing efficiency and more stable model predictions, especially for small sample sizes. Furthermore, the Bayesian methods with informative priors performed better (smaller values of deviance information criterion (DIC)) than those with the non-informative priors. Therefore, our results demonstrated the advantages of applying the Bayesian methods on the SUR biomass models, not only obtaining better model fitting and predictions, but also offering the assessment and evaluation of the uncertainties for constructing and updating tree biomass models.