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基于贝叶斯方法的蒙古栎林单木枯死模型

姚丹丹 徐奇刚 闫晓旺 李玉堂

姚丹丹, 徐奇刚, 闫晓旺, 李玉堂. 基于贝叶斯方法的蒙古栎林单木枯死模型[J]. 北京林业大学学报, 2019, 41(9): 1-8. doi: 10.13332/j.1000-1522.20180260
引用本文: 姚丹丹, 徐奇刚, 闫晓旺, 李玉堂. 基于贝叶斯方法的蒙古栎林单木枯死模型[J]. 北京林业大学学报, 2019, 41(9): 1-8. doi: 10.13332/j.1000-1522.20180260
Yao Dandan, Xu Qigang, Yan Xiaowang, Li Yutang. Individual-tree mortality model of Mongolian oak forests based on Bayesian method[J]. Journal of Beijing Forestry University, 2019, 41(9): 1-8. doi: 10.13332/j.1000-1522.20180260
Citation: Yao Dandan, Xu Qigang, Yan Xiaowang, Li Yutang. Individual-tree mortality model of Mongolian oak forests based on Bayesian method[J]. Journal of Beijing Forestry University, 2019, 41(9): 1-8. doi: 10.13332/j.1000-1522.20180260

基于贝叶斯方法的蒙古栎林单木枯死模型

doi: 10.13332/j.1000-1522.20180260
基金项目: 林业行业公益性科研项目(201504303)
详细信息
    作者简介:

    姚丹丹。主要研究方向:森林经理学。Email:371352079@qq.com  地址:100091北京市海淀区香山路东小府1号中国林业科学研究院资源信息研究所

    责任作者:

    闫晓旺,教授级高级工程师。主要研究方向:森林经理学。Email:ccyxw2005@163.com  地址:130022吉林省长春市人民大街4756号吉林省林业调查规划院

  • 中图分类号: S758.5

Individual-tree mortality model of Mongolian oak forests based on Bayesian method

  • 摘要: 目的贝叶斯统计法在提高模型参数稳定性上有较大的优势,研究贝叶斯方法在单木枯死模型中的应用,改进模型参数的估计方法,为蒙古栎天然林林分生长收获与经营管理提供参考。方法以蒙古栎天然异龄林为对象,基于202块固定样地数据,利用二分类Logistic模型构建基于经典概率统计法、贝叶斯法和分层贝叶斯法的蒙古栎单木枯死模型。随机抽取80%的数据用于建立模型,剩下的20%用于检验模型,利用经典概率统计法(非线性最小二乘法)、有先验信息的贝叶斯统计法和无先验信息的分层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计算ROC曲线下的面积AUC(Under Curve)来判断,并利用Pearson-χ2检验来检验模型的拟合优度。结果(1)贝叶斯法与传统极大似然法的估计值相近,且其估计参数的标准差小于传统方法。(2)贝叶斯法估计参数的可信区间最小,比传统极大似然法的置信区间小6.0% ~ 31.8%。层次贝叶斯法估计参数的可信区间最大,比传统极大似然法的置信区间大11.2% ~ 185.0%。(3)拟合效果最好的是层次贝叶斯法,其模型AUC值为0.83,贝叶斯法与传统极大似然法模型的AUC值均为0.73。结论层次贝叶斯法在拟合枯死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。

     

  • 图  1  单木枯死模型参数的贝叶斯估计的95%可信区间

    C:极大似然法;B:贝叶斯法;HB:层次贝叶斯法。下同。C represents estimated results of maximum likelihood method; B represents estimated results of Bayesian method; HB represents estimated results of Hierarchical Bayesian method. Same as below.

    Figure  1.  Bayesian 95% credible and classical 95% confidence intervals for parameters in mortality mode

    图  2  枯死模型的贝叶斯、层次贝叶斯参数的后验分布和极大似然估计参数的似然分布

    Figure  2.  Posterior distribution of Bayesian method and likelihood distribution of maximum likelihood method for morality model

    图  3  3种方法拟合枯死模型的ROC曲线

    Figure  3.  ROC curves of mortality model based on three methods

    表  1  建模数据和检验数据样地基本因子统计量

    Table  1.   Summary statistics of sample plots for calibration and validation data

    项目
    Item
    株数
    Number of trees
    自变量
    Independent variable
    平均值
    Average
    最大值
    Maximum
    最小值
    Minimum
    标准差
    Standard deviation
    建模数据 Calibration data 11 118 D 12.386 5 86.806 5 5.000 0 7.456 7
    BAL 0.846 3 2.040 9 0.000 0 0.397 1
    N 1 599 3 950 467 675
    Nm 135 733 17 134
    检验数据 Validation data 2 780 D 12.155 9 73.690 9 5.003 6 7.440 2
    BAL 0.841 0 1.881 1 0.000 0 0.390 6
    N 1 482 3 950 217 698
    Nm 202 700 17 135
    注:D为林木胸径(cm),BAL为林木胸高断面积(m2/hm2),N为林分密度(株/hm2),Nm为林分枯死株数(株/hm2)。Notes: D represents DBH (cm); BAL represents basal area of breast height of forest trees (m2/ha); N represents stand density (tree/ha); Nm represents number of dead trees (tree/ha).
    下载: 导出CSV

    表  2  参数的先验信息

    Table  2.   Prior distribution of each parameter for base model and mixed-effects model

    模型 Model参数 Parameter先验分布 Prior distribution
    基础模型
    Base model
    a0 a0 ~ N (−2.148 3, 0.149 52)
    a1 a1 ~ N (−0.126, 0.010 52)
    a2 a2 ~ N (1.294 3, 0.093 92)
    a3 a3 ~ N (0.176 3, 0.007 32)
    a4 a4 ~ N (−1.893 9, 0.444 82)
    混合模型
    Model with
    random effects
    a0 a0 ~ N (0, 10 002)
    a1 a1 ~ N (0, 10 002)
    a2 a2 ~ N (0, 10 002)
    a3 a3 ~ N (0, 10 002)
    a4 a4 ~ N (0, 10 002)
    σa0 (1/σa0)2 ~ Gamma (0.001, 0.001)
    σ (1/σ)2 ~ Gamma (0.001, 0.001)
    下载: 导出CSV

    表  3  观测值和预测值的列联表

    Table  3.   Contingency table of the observed values and predicted one

    项目 Item预测值 Predicted value总和 Total
    枯死 Dead存活 Alive
    观测值 Observed value 枯死 Dead a11 a12 A1m
    存活 Alive a21 a22 A2m
    和 Total An1 An2 Anm
    敏感度 Sensitivity=a11/A1m, 特异度 Specificity=a22/A2m
    注:a11表示正确预测枯死林木的株数,a12表示错误预测枯死林木的株数,a21表示错误预测林木存活的株数,a22表示正确预测存活林木的株数,A1m表示枯死实测值,A2m表示存活实测值,An1表示枯死预测值,An2表示存活预测值。Notes: a11 represents the number of dead trees which is correctly predicted, a12 represents the number of dead trees which is not correctly predicted, a21 represents the number of alive trees which is not correctly predicted, a22 represents the number of alive trees which is correctly predicted, A1m represents the measured value of dead trees, A2m represents the measured value of alive trees, An1 represents the predicted value of dead trees, An2 represents the predicted value of alive trees.
    下载: 导出CSV

    表  4  基于建模数据的参数估计结果

    Table  4.   Parameter estimates of classical and Bayesian methods using calibration

    方法
    Method
    参数
    Parameter
    估计值
    Estimated value
    标准差
    Standard deviation
    置信区间 Credible interval
    2.50%97.50%
    最大似然 Maximum likelihood a0 −2.148 3 0.149 5 −2.447 2 −1.849 4
    a1 −0.126 0 0.010 5 −0.147 1 −0.104 9
    a2 1.294 3 0.093 9 1.106 6 1.482 1
    a3 0.176 3 0.073 2 0.029 8 0.322 8
    a4 −1.893 9 0.444 8 −2.783 5 −1.004 3
    贝叶斯统计 Bayesian method a0 −2.136 0 0.138 8 −2.413 6 −1.858 4
    a1 −0.123 1 0.007 2 −0.137 5 −0.108 7
    a2 1.271 0 0.078 8 1.113 3 1.428 7
    a3 0.136 1 0.062 3 0.011 6 0.260 6
    a4 −1.886 0 0.415 4 −2.716 8 −1.055 2
    层次贝叶斯 Hierarchical bayesian method a0 −2.641 0 0.289 7 −3.248 0 −2.176 0
    a1 −0.145 4 0.013 0 −0.168 6 −0.118 0
    a2 1.595 0 0.176 0 1.311 0 1.963 0
    a3 0.274 8 0.084 9 0.108 7 0.444 0
    a4 −3.082 0 1.337 0 −5.523 0 −0.452 2
    σa0 1.030 0 0.158 9 0.742 8 1.360 0
    下载: 导出CSV

    表  5  3种方法拟合的枯死模型误差统计量

    Table  5.   Error statistics of morality model by three methods

    方法 Method建模数据 Calibration data验证数据 Validation data
    枯死数
    Number of
    dead trees
    预测枯死数
    Predicted number
    of dead trees
    χ2AUCAIC (DIC)枯死数
    Number of
    dead trees
    预测枯死数
    Predicted number
    of dead trees
    χ2AUC (DIC)
    传统方法
    Classical method
    1 338 1 349 0.09 0.734 7 407.4 375 404 2.08 0.726
    贝叶斯统计
    Bayesian method
    1 338 1 336 0.01 0.734 7 407.21 375 394 0.92 0.727
    层次贝叶斯统计
    Hierarchical Bayesian method
    1 338 1 335 0.01 0.825 6 771.26 375 389 0.50 0.800
    下载: 导出CSV
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出版历程
  • 收稿日期:  2018-08-07
  • 修回日期:  2019-01-25
  • 网络出版日期:  2019-09-09
  • 刊出日期:  2019-09-01

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