基于贝叶斯方法的蒙古栎林单木枯死模型

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

【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。

[Objective]The Bayesian method is preponderant on improving the stability of model parameters.This paper explores the application of Bayesian method in the individual-tree mortality model and the improvement of estimation method of model parameters to provide reference for the growth and yield of Mongolian oak natural forests.[Method]With the data of 202 Mongolian oak forest permanent sample plots,we developed individual-tree mortality model based on logistic model using classical method,Bayesian method and hierarchical Bayesian method.A random sample of 80%data was used for model calibration,and the remaining 20%was used for model validation.We developed individual-tree mortality model based on logistic model using classical method,Bayesian method and hierarchical Bayesian method,Bayesian statistics with prior and hierarchical Bayesian method with uninformative prior.Models were evaluated by calculating AUC(area under ROC curve)and Pearson-χ2 test.[Result]The results showed that:(1)the parameter estimated values of classical method and Bayesian method were similar,and the standard deviation of Bayesian statistics was smaller than classical method.(2)The confidence intervals of the 3 parameter estimation methods had a large coincidence.Bayesian method with informative prior had the smallest confidence interval,which was 6.0%-31.8%smaller than confidence interval of classical method.The confidence interval of hierarchical Bayesian method was more dispersed,which was 11.2%-185.0%larger than classical method.(3)The model of hierarchical Bayesian method had the best goodness of fit.The values of AUC of classical method and Bayesian method were 0.73,and the AUC value of hierarchical Bayesian method was 0.83.It is indicated that the results of the three methods are statistically significant.[Conclusion]The hierarchical Bayesian method has obvious advantages in fitting the individual-tree mortality model,whose performance is the best,and the model has the highest prediction accuracy.