[Constructing biomass models for natural Quercus mongolica based on Bayesian seemingly unrelated regression]

In this study, the biomass models for natural Quercus mongolica in Heilongjiang Province were constructed based on the predictors of diameter at breast height (D) and tree height (H) by several methods including multivariate likelihood analysis and seemingly unrelated regression. The results showed that the H could significantly improve the stem biomass model, with the coefficient of determination (R²) being increased from 0.953 to 0.988 and the root mean square error (RMSE) being reduced by 14 kg, but it had no significant improvement for the biomass model of branch, foliage, and root. The error structures of both biomass model systems (only D and D-H) were multiplicative, indicating that the linear models after logarithmic transformation were more appropriate. The R² for the biomass models of stem, branch, foliage and root were 0.953-0.988, 0.982-0.983, 0.916-0.917, and 0.951-0.952, while the RMSE were 13.42-27.03, 6.84-7.00, 1.95-1.97 and 9.71-9.84 kg. Compared with the feasible generalized least squares (FGLS) approach, Bayesian estimation had similar fitting performance and provided parameter estimates with different variations. The standard errors of parameters for FGLS were 0.054-0.211. There were similar variations (standard deviations of 0.055-0.221) for the two Bayesian estimation with no prior information (DMC and Gibbs1). The Gibbs sampler with a multivariate normal distribution with a mean vector of 0, variances of 1000 and covariances of 0 (Gibbs2) or the prior information from the historical researches summary for Quercus trees biomass models (Gibbs3) produced greater variation than those of FGLS, DMC, and Gibbs1 (stan-dard deviations were 0.080-0.278), while Gibbs sampler with the prior information obtained from own data (Gibbs4) provided the lower variations than others (standard deviations were 0.004-0.013). The Gibbs4 approach provided the narrowest 95% prediction interval and produced the smaller prediction biases, with the average absolute error percentage (MAPE) for stem, branch, foliage, root and total of the only-D biomass model being 19.8%, 24.7%, 24.6%, 29.0% and 13.1%, while MAPE for the corresponding components of D-H biomass model kept same except for stem and total decreased to 10.5% and 9.8%, which indicated that Gibbs4 could provide more accurate biomass predictions. Compared with classical statistics, accurate prior information made Bayesian seemingly unrelated regression an advantage in estimation stability and uncertainty reduction.