【目的】贝叶斯统计法在提高参数稳定性上有较大的优势,但在森林生长模型中的应用并不多见。研究贝叶斯方法在树高-胸径模型中的应用,改进模型参数的估计方法,为蒙古栎天然林树高生长预测提供支持。【方法】以蒙古栎天然异龄林为对象,基于197块蒙古栎天然异龄林固定样地数据,采用传统极大似然法、贝叶斯法估计树高-胸径基础模型,以及极大似然法与层次贝叶斯法估计树高-胸径混合效应模型。随机抽取80%的样地数据用于建立模型,剩余的20%用于检验模型,基于基础模型与混合效应模型,利用经典概率统计法(极大似然估计)、有先验信息的贝叶斯统计法和层次贝叶斯统计法进行参数估计,分析模型的表现和参数分布。模型的拟合效果通过绝对平均误差(MAE)、相对平均误差(RME)、均方根误差(RMSE)、相对均方根误差(RMSE%)、决定系数(R²)、赤池信息准则(AIC)和偏差信息准则(DIC)指标来确定。【结果】对于基础模型,有先验信息的贝叶斯统计参数可信区间集中。对于混合模型,层次贝叶斯法估计的固定效应参数可信区间较传统方法更为集中,但随机效应参数可信区间相较极大似然法的置信区间更为扩散。使用层次贝叶斯混合效应模型的拟合效果最好,其决定系数R²为0.946。MAE、RMSE和RMSE%指标显示,层次贝叶斯法估计的模型精度最高,其次为极大似然估计的混合效应模型,贝叶斯法估计的基础模型以及极大似然估计的基础模型精度较低。【结论】层次贝叶斯统计法在拟合树高-胸径模型方面具有明显的优势,拟合效果最好,模型预估精度最高。此外,层次贝叶斯法能够以之前建立的模型结果作为先验信息而建立新的模型,是森林经营单位更新模型的可选方法之一。

【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.