基于贝叶斯法的长白落叶松林分优势高生长模型研究
Bayesian parameter estimation of dominant height growth model for Changbai larch (Larix olgensis Henry) plantations
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摘要: 贝叶斯统计推断是基于总体信息、样本信息和先验信息的一种统计推断方法,并已成为森林生长模型中的一种重要方法。本文以长白落叶松人工林为对象,基于1 687对林分优势高与年龄数据,利用Richards生长方程构建基于贝叶斯法和经典概率统计法的林分优势高生长模型,探讨贝叶斯统计法拟合小样本量数据的稳定性。分别基于全部样本,以及随机抽取的10%、5%和2%样本,利用经典概率统计法(非线性最小二乘法)、无先验信息的贝叶斯统计法和有先验信息的贝叶斯统计法进行参数估计,分析模型表现和参数分布。模型评价指标包括均方根误差(RMSE)、贝叶斯统计常用的DIC统计值以及参数的可信区间。结果表明:基于小样本的贝叶斯统计与大样本的经典概率统计的拟合结果相近,但贝叶斯统计法估计的参数稳定性强,且抽样5%时的RMSE值最小。有先验信息的贝叶斯统计拟合结果优于无先验信息的贝叶斯统计拟合结果,参数分布也较为集中,不确定性小;有先验信息贝叶斯统计和经典概率统计的参数分布区间有较大重叠。另外,有先验信息贝叶斯统计对3种不同样本量的拟合结果显示,参数标准差以及模型RMSE值都是在抽样5%时最小,说明用贝叶斯统计的拟合精度及参数确定性与样本量大小也有一定关系。研究验证了贝叶斯统计在利用先验信息、基于小样本量进行森林生长建模时的优越性。Abstract: Bayesian inference is an alternative method of statistical inference based on prior and data information. It has become an important statistical method for forest growth modeling. With 1 687 pairs of the dominant height and age data of Changbai larch (Larix olgensis Henry) plantations, we developed dominant height-age model based on Richards equation by using classical and Bayesian methods, and discussed model reliability with small sample size and Bayesian method. To test model performance for small sample size, four sample size options were employed including all data,10%, 5% and 2% of all sample randomly selected. We examined model performance and the distribution of parameters among methods for parameter estimation covering classical statistics (nonlinear least squares method), Bayesian statistics with uninformative prior and informative prior. Models were evaluated by root mean square error (RMSE), DIC and the confidence intervals of parameters. Results showed that the results of Bayesian statistics with small sample size was very close to those of classical statistics with large sample size, while the model reliability using Bayesian method was better than classical method, and RMSE with 5% sample was the smallest. Bayesian method with informative priors has the best performance for 5% sample. Compared with non-informative priors, the fitting results by Bayesian with informative priors were better, distribution was more concentrated and it had less uncertainty. The distribution of parameters estimated from Bayesian method with informative prior was largely overlapped with that from classical method. In addition, the results of Bayesian statistics with informative priors based on three different sample sizes showed that both the standard deviations of parameters and the RMSE of model were the smallest with 5% sample. It indicated that the fitting precision of Bayesian statistics and parameters uncertainty also had a certain relationship with sample size. The study confirmed the advantages of Bayesian method in model parameter estimation of forest growth for small sample size and using informative priors.