基于贝叶斯法的新疆天山云杉树高-胸径模型研究  

Tree height-DBH model for Picea schrenkiana in Tianshan Mountain, Xinjiang ofnorthwestern China based on Bayesian method

作　　者：邓祥鹏 许芳泽 赵善超 向玮 Deng Xiangpeng;Xu Fangze;Zhao Shanchao;Xiang Wei(College of Forestry and Landscape Architecture,Xinjiang Agricultural University,Urumqi 830052,Xinjiang,China;Key Laboratory of Forest Resources and Environmental Management of National Forestry and Grassland Administration,Beijing Forestry University,Beijing 100083,China;Natural Forest Protection Center of Uygur Autonomous Region of Xinjiang,Urumqi 830000,Xinjiang,China)

机构地区：[1]新疆农业大学林学与风景园林学院,新疆乌鲁木齐830052 [2]北京林业大学森林资源和环境管理国家林草局重点实验室,北京100083 [3]新疆维吾尔自治区天然林保护中心,新疆乌鲁木齐830000

出　　处：《北京林业大学学报》2023年第1期11-20,共10页Journal of Beijing Forestry University

基　　金：新疆维吾尔自治区财政林业科技项目(新林规字〔2022〕9号);国家自然科学基金项目(32160366)。

摘　　要：【目的】贝叶斯统计法能够利用先验信息与样本信息去进行统计推断,可有效提升模型参数的可靠程度和稳定性。【方法】本研究以天山云杉林为研究对象,使用3块100 m×100 m天山云杉调查样地数据,利用经典统计方法(极大似然法)、贝叶斯法构建天山云杉树高−胸径模型。利用随机抽样法抽取80%样地数据进行建模,20%样地数据进行检验,对比分析基于经典方法的非线性模型和非线性混合效应模型以及基于贝叶斯法的贝叶斯模型和层次贝叶斯模型的表现和参数分布。【结果】通过对比非线性模型和贝叶斯模型,贝叶斯模型的a、b、c 3个参数置信区间比非线性模型的分别要窄53.86%、46.87%、65.17%。而层次贝叶斯模型和非线性混合效应模型相比,层次贝叶斯模型的固定效应参数置信区间比非线性混合效应模型的要窄37.21%、62.62%、49.31%,但随机效应参数标准差的置信区间更为分散。基于贝叶斯法的模型,其参数标准差均低于基于经典方法的模型。4种树高−胸径模型的拟合结果显示:层次贝叶斯模型的拟合效果优于其他3种模型,其决定系数(R2)为0.961。拟合精度显示:层次贝叶斯模型的预测精度略高于非线性混合效应模型。【结论】两种混合模型虽然在拟合结果上没有明显区别,但与非线性混合效应模型相比,层次贝叶斯模型在参数估计的稳定性上更好,其预测更具可靠性。[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 es

关 键 词：树高−胸径关系 贝叶斯法 层次贝叶斯模型 天山云杉 

分 类 号：S791.247[农业科学—林木遗传育种]