Abstract:

【Objective】 Bayesian methods have advantages with regards to improving parameter stability. In this study, we examined the application of Bayesian methodology in tree height-diameter modeling, and improved the estimation method used for Mongolian oak (Quercus mongolica) forest height growth prediction. 【Method】 Utilizing the data obtained from 197 Mongolian oak forest permanent sample plots, we developed a height-diameter model using a classical statistical method, a Bayesian method, and a hierarchical Bayesian method. A random sample of 80% of the data was used for model calibration, and the remaining 20% was used for model validation. We tested model performance and the distribution of parameters among methods for parameter estimation, covering classical statistics (maximum likelihood method), Bayesian statistics with informative prior, and hierarchical Bayesian statistics with uninformative prior. Models were evaluated by calculating the absolute average error (MAE), relative average error (RME), root mean square error (RMSE), relative root mean square error (RMSE%), R², akaike information criterion (AIC), and deviation information criterion (DIC). 【Result】 The confidence intervals of Bayesian statistics with informative prior were concentrated, with the intervals of its three parameters lower than those of the maximum likelihood method. With the inclusion of random effects, the confidence interval of the fixed-effect parameters of the hierarchical Bayesian method was lower than that of the maximum likelihood estimation parameter, and the confidence interval of the standard deviation of the random effect parameters was higher than that of the maximum likelihood method. The hierarchical Bayesian method showed the best performance, with anR² value of 0.946. On the bases of MAE, RMSE and RMSE% values, the prediction accuracy of the hierarchical Bayesian method was the highest, followed by the maximum likelihood method with random effects, the Bayesian method with informative prior, and the maximum likelihood method. 【Conclusion】 The hierarchical Bayesian statistical method has obvious advantages with respect to the best fitting of the tree height-diameter model, and the model had the highest prediction accuracy. In addition, it can use prior information to establish a new model using the previously established model results, which can be used an alternative method for forest management departments updating models.

Key words: natural uneven-aged Mongolian oak (Quercus mongolica) forest, individual diameter-height model, maximum likelihood estimation, hierarchical Bayesian statistics