Construction of biomass models for <i>Larix olgensis</i> plantation using hierarchical Bayesian seemingly unrela-ted regression.

Accurate estimation of forest biomass is of great significance for carbon stock assessment and forest resource management. Hierarchical Bayesian methods, as a statistical approach that can effectively enhance parameter stability, have large potentials in the precise estimation of forest biomass. Based on data from 143 sample trees of <i>Larix olgensis</i> in the Mengjiagang Forest Farm of Heilongjiang Province, we adopted hierarchical Bayesian see-mingly unrelated regression (SUR) to develop a univariate seemingly unrelated mixed-effects model (SURM1) with diameter at breast height (DBH) as the independent variable and a bivariate seemingly unrelated mixed-effects model (SURM2) with DBH and tree height as independent variables. We compared the fitting and predictive performance of restricted maximum likelihood estimation (REML) with three hierarchical Bayesian methods: no prior information (Br1), data-derived prior information (Br2), and historical prior information (Br3). The results showed that the SURM2 model significantly outperforms SURM1 in predicting stem biomass and total individual tree biomass, with mean absolute percentage errors (MAPE) reduced by 7.8% and 7.6%, respectively. The hierarchical Bayesian method utilizing data-derived prior information (Br2) demonstrated notably superior parameter estimation stability (with standard deviations ranging from 0.003 to 0.108) compared to REML (standard deviations from 0.052 to 0.540), Br1 (standard deviations from 0.033 to 0.819), and Br3 (standard deviations from 0.038 to 0.771). Predictions based on Br2 yield superior accuracy, with MAPE for SURM1 model predictions of stem, branch, leaf, root, and total biomass being 17.6%, 45.1%, 48.3%, 25.2%, and 17.1%, respectively. The SURM2 model improved the prediction accuracy for stem biomass and total biomass, reducing MAPE by 7.3% and 6.7%, respectively, compared to SURM1. Furthermore, when sample size was small (fewer than 60), incorporating effective prior information could enhance the stability of predictions. The use of data-derived prior information in the Bayesian method demonstrated significant advantages in improving both the accuracy and stability of biomass predictions for <i>L. olgensis</i>, providing valuable support for the precise estimation of biomass in the Heilongjiang Pro-vince.