Objective Bayesian statistics can use prior information and sample information to make statistical inference, which can effectively improve the reliability and stability of model parameters.
Method The data were obtained from three 100 m × 100 m sample plots of Picea schrenkiana, and the classical statistical method (maximum likelihood method) and Bayesian method were used to construct the tree height-DBH model of Picea schrenkiana. 80% of the sample plot data were randomly selected for modelling, and 20% of the sample plot data were validated to compare and analyze the performance and parameter distribution of the non-linear model and non-linear mixed effect model based on the classical method and the Bayesian model and Hierarchical Bayesian model based on the Bayesian method.
Result By comparing the non-linear model and Bayesian model, the confidence intervals for the three parameters a, b and c of the Bayesian model were 53.86%, 46.87% and 65.17% narrower than those of the non-linear model, respectively. In contrast, the confidence intervals for the fixed effect parameters of the Hierarchical Bayesian model were 37.21%, 62.62% and 49.31% narrower than those of the non-linear mixed effect model, respectively, but the confidence intervals for the SD of the random effect parameters were more spread out compared with those of the Hierarchical Bayesian model and the non-linear mixed effect model. The models based on the Bayesian approach all had lower parameter SD than those based on the classical approach. The fitting results of the four tree height-DBH models showed that the Hierarchical Bayesian model fitted better than the other three models, with a coefficient of determination (R2) of 0.961. The fitting accuracy showed that the prediction accuracy of the Hierarchical Bayesian model was slightly higher than that of the non-linear mixed effect model.
Conclusion Although there is no significant difference between the two mixed models in terms of fitting results, the Hierarchical Bayesian model is better in terms of stability of parameter estimation and its prediction is more reliable compared with the non-linear mixed effect model.