基于贝叶斯方法的蒙古栎林单木树高-胸径模型

doi:10.3969/j.issn.1000-2006.201901031

国家林草科技领军期刊
中国精品科技期刊
中国高校百佳科技期刊
江苏省新闻出版政府奖期刊奖
RCCSE林学权威期刊（A+）
CSCD核心期刊
Scopus数据库收录期刊
中文核心期刊
SCD核心期刊

作者加群：102861116

微信公众号：南京林业大学学报

高级检索

南京林业大学学报（自然科学版） ›› 2020, Vol. 44 ›› Issue (1): 131-137.doi: 10.3969/j.issn.1000-2006.201901031

基于贝叶斯方法的蒙古栎林单木树高-胸径模型

姚丹丹¹(), 徐奇刚¹, 闫晓旺²^,^*(), 李玉堂²

1.中国林业科学研究院资源信息研究所,北京 100091
2.吉林省林业调查规划院吉林长春 130022

收稿日期:2019-01-22 修回日期:2019-06-15 出版日期:2020-02-08 发布日期:2020-02-02
通讯作者: 闫晓旺
作者简介:姚丹丹( danil55@icloud.com)。
基金资助:
国家林业行业公益性科研专项项目(201504303)

Individual diameter-height model for Mongolian oak forests based on Bayesian method

YAO Dandan¹(), XU Qigang¹, YAN Xiaowang²^,^*(), LI Yutang²

1. Insititute of Forest Resource Information Techniques,Chinese Academy of Forestry,Beijing 100091,China
2. Jilin Forestry Inventory and Planning Institute, Changchun 130022,China

Received:2019-01-22 Revised:2019-06-15 Online:2020-02-08 Published:2020-02-02
Contact: YAN Xiaowang

摘要/Abstract

摘要：

【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。

关键词: 蒙古栎天然异龄林, 树高-胸径模型, 最大似然法, 层次贝叶斯统计

Abstract:

【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.

Key words: natural uneven-aged Mongolian oak (Quercus mongolica) forest, individual diameter-height model, maximum likelihood estimation, hierarchical Bayesian statistics

中图分类号:

S758.3

姚丹丹,徐奇刚,闫晓旺,等. 基于贝叶斯方法的蒙古栎林单木树高-胸径模型[J]. 南京林业大学学报（自然科学版）, 2020, 44(1): 131-137.

YAO Dandan, XU Qigang, YAN Xiaowang, LI Yutang. Individual diameter-height model for Mongolian oak forests based on Bayesian method[J].Journal of Nanjing Forestry University (Natural Science Edition), 2020, 44(1): 131-137.DOI: 10.3969/j.issn.1000-2006.201901031.

图/表 6

表1

表2

表3

图1

表4

表5

参考文献 23

[1]	张雄清, 张建国, 段爱国. 基于贝叶斯法估计杉木人工林树高生长模型[J]. 林业科学, 2014, 50(3):69-75.
	ZHANG X Q, ZHANG J G, DUAN A G. Tree-height growth model for Chinese fir plantation based on Bayesian method[J]. Scientia Silvae Sinicae, 2014, 50(3):69-75. DOI: 10.11707/j.1001-7488.20140310. doi: 10.11707/j.1001-7488.20140310
[2]	卢军, 张会儒, 雷相东, 等. 长白山云冷杉针阔混交林幼树树高——胸径模型[J]. 北京林业大学学报, 2015, 37(11):10-25.
	LU J, ZHANG H R, LEI X D, et al. Height-diameter models for saplings in a spruce-fir mixed forest in Changbai Mountains[J]. Journal of Beijing Forestry University, 2015, 37(11):10-25. DOI: 10.13332/j.1000-1522.20140429. doi: 10.13332/j.1000-1522.20140429
[3]	BOX G E P, TIAO G C. Bayesian inference in statistical analysis[M]. Massachusetts: Wiley Press, 1992:52-65.
[4]	SEBER G A F, WILD C J. Nonlinear regression [M]. Massachusetts: Wiley Press, 1989:188-164.
[5]	WYCKOFF P H, CLARK J S. Predicting tree mortality from diameter growth: a comparison of maximum likelihood and Bayesian approaches[J]. Canadian Journal of Forest Research, 2000, 30(1):156-167. doi: 10.1139/x99-198
[6]	METCALF C J E, MCMAHON S M, CLARK J S. Overcoming data sparseness and parametric constraints in modeling of tree mortality: a new nonparametric Bayesian model[J]. Canadian Journal of Forest Research, 2009, 39(9):1677-1687.DOI: 10.1139/X09-083. doi: 10.1139/X09-083
[7]	GREEN E J, ROESCH F A. Bayesian estimation for the three-parameter Weibull distribution with tree diameter data[M]. Washington, DC, ETATS-UNIS: International Biometric Society, 1994:110-152.
[8]	BULLOCK B P, BOONE E L. Deriving tree diameter distributions using Bayesian model averaging[J]. Forest Ecology and Management, 2007, 242(2/3):127-132.DOI: j.foreco.2007.01.024. doi: j.foreco.2007.01.024
[9]	LI R X, STEWART B, WEISKITTEL A. A Bayesian approach for modelling non-linear longitudinal/hierarchical data with random effects in forestry[J]. Forestry, 2012, 85(1):17-25. DOI: 10.1093/forestry/cpr050. doi: 10.1093/forestry/cpr050
[10]	GREEN E J, STRAWDERMAN W E. A Bayesian growth and yield model for slash pine plantations[J]. Journal of Applied Statistics, 1996, 23(2/3):285-300.DOI: 10.1080/02664769624251. doi: 10.1080/02664769624251
[11]	NYSTROM K, STAHL G. Forecasting probability distributions of forest yield allowing for a Bayesian approach to management planning[J]. Silva Fennica, 2001, 35(2):185-201.DOI: 10.14214/sf.595. doi: 10.14214/sf.595
[12]	ZHANG X Q, DUAN A G, ZHANG J G. Estimating Height-diameter models with Bayesian method[J]. The Scientific World Journal 2014(1):1-9.DOI: 10.1155/2014/683691. doi: 10.1155/2014/683691
[13]	WYCKOFF P H, ClARK J S. Predicting tree mortality from diameter growth: a comparison of maximum likelihood and Bayesian approaches[J]. Canadian Journal of Forest Research, 2000, 30(1):156-167.DOI: 10.1139/x99-198. doi: 10.1139/x99-198
[14]	姚丹丹, 雷相东, 张则路. 基于贝叶斯法的长白落叶松林分优势高生长模型研究[J]. 北京林业大学学报, 2015, 37(3):94-100.
	YAO D D, LEI X D, ZHANG Z L. Bayesian parameter estimation of dominant height growth model for Changbai larch (Larix olgensis Henry) plantations [J]. Journal of Beijing Forestry University, 2015, 37(3):94-100. DOI: 10.13332/j.1000-1522.20140221. doi: 10.13332/j.1000-1522.20140221
[15]	ZHANG X Q, CAO Q V, DUAN A G, et al. Modeling tree mortality in relation to climate, initial planting density, and competition in Chinese fir plantations using a Bayesian logistic multilevel method.[J]Canadian Journal of Forest Research, 2017, 47(9):1278-1285.DOI: 10.1139/cjfr-2017-0215. doi: 10.1139/cjfr-2017-0215
[16]	ZHANG X Q, ZHANG J G, DUAN A G, et al. A hierarchical Bayesian model to predict self-thinning line for Chinese fir in southern China[J]. PLoS ONE, 2015, 10(10):e0139788.DOI: 10.1371/journal.pone.0139788. doi: 10.1371/journal.pone.0139788
[17]	马武. 蒙古栎林单木生长模型系研究[D]. 北京:中国林业科学研究院, 2012.
	MA W. Individual tree growth model system for Mongolian oak forest[D]. Beijing: Chinese Academy of Forestry, 2012.
[18]	LI R X, STEWART B, WEISKITTEL A. A Bayesian approach for modelling non-linear longitudinal/hierarchical data with random effects in forestry[J]. Forestry, 2012, 85(1):17-25.DOI: 10.1093/forestry/cpr050. doi: 10.1093/forestry/cpr050
[19]	RUSSELL M B. Influence to prior distributions and random effects on count regression models: implications for estimating standing dead tree abundance[J]. Environment and Ecological Statistics, 2015, 22:145-160.DOI: 10.1007/s10651-014-0290-7. doi: 10.1007/s10651-014-0290-7
[20]	PATENAUD G, MILNE R. Integrating remote sensing datasets into ecological modelling: a Bayesian approach[J]. International Journal of Remote Sensing, 2008, 29(5):1295-1315.DOI: 10.1080/01431160701736414. doi: 10.1080/01431160701736414
[21]	FANG S, GERTNER G. Analysis of parameters of two growth models estimated using Bayesian methods and nonlinear regression[R/EB]. http://Cmsi.gre.ac.uk./conferences/iufro (proceedings)( 2004).
[22]	KLEMEDTSSON L, JANSSON P E, et al. Bayesian calibration method used to elucidate carbon turnover in forest on drained organic soil[J]. Biogeochemistry, 2008, 89(1):61-79.DOI: 10.1007/s10533-007-9169-0. doi: 10.1007/s10533-007-9169-0
[23]	RITCHIE M W, HANN D W. Development of a tree height growth model for Douglas-fir[J]. Forest Ecology and Management, 1986, 15(2):135-145.DOI: 10.1016/0378-1127(86)90142-8. doi: 10.1016/0378-1127(86)90142-8

统计量 statistics	建模数据calibration data			检验数据validation data
统计量 statistics	H/m	H₀/m	D/cm	H/m	H₀/m	D/cm
平均值 average	14.84	17.6	15.94	15.14	17.74	16.13
最大值 max.	24.00	27.00	27.90	19.00	22.00	24.60
最小值 min.	8.00	11.00	6.20	9.00	12.00	9.20
标准差 standard deviation	2.49	2.54	3.61	2.30	2.35	3.44
变异系数 coefficient of variation/%	16.78	14.43	22.64	15.19	13.25	21.33

模型 model	参数 parameter	先验分布 prior distribution
基础模型 base model	α	α~N(1.67,0.20²)
	β	b~N(0.83,0.04²)
	γ	c~N(4.34,0.35²)
混合模型 mixed effect model	α	α~N(1.53,0.19²)
	β	b~N(0.86,0.04²)
	γ	c~N(4.32,0.38²)
	σ_b	(1/σ_b)² ~γ(0.001,0.001)
	σ_c	(1/σ_c)² ~γ(0.001,0.001)
	Σ	(1/σ)²~γ(0.001,0.001)

方法 method	参数 parameter	均值 average	标准差 standard deviation	置信区间 credible interval
方法 method	参数 parameter	均值 average	标准差 standard deviation	2.50%	97.50%
极大似然法 (基础模型) maximum likelihood (base model)	α	1.67	0.20	1.27	2.06
	β	0.83	0.04	0.76	0.90
	γ	4.34	0.35	3.64	5.04
贝叶斯统计 (基础模型) Bayesian statistic (base model)	α	1.74	0.10	1.57	1.94
	β	0.82	0.02	0.78	0.85
	γ	4.41	0.21	4.03	4.82
极大似然法 (混合模型) maximum likelihood (mixed effect model)	α	1.53	0.19	1.15	1.90
	β	0.86	0.04	0.78	0.93
	γ	4.33	0.38	3.59	5.07
	σ_b	0.01		0.01	0.02
	σ_c	0.39		0.15	0.98
层次贝叶斯统计 (混合模型) hierarchical Bayesian statistics (mixed effect model)	α	0.30	0.01	0.28	0.31
	β	0.84	0.01	0.83	0.85
	γ	3.57	0.37	2.74	4.28
	σ_b	0.58	1.74	0.52	0.65
	σ_c	4.80	11.29	4.08	5.69

方法method	σ(MAE)	σ(RME)	σ(RMSE)	σ(RMSE%)	R²	AIC	DIC
极大似然估计(基础模型) max. likelihood (base model)	0.67	0.49	1.09	7.84	0.848	1 051.67
贝叶斯统计(基础模型) Bayesian statistics (base model)	0.66	-0.05	1.00	7.36	0.838		1 049.13
极大似然估计(混合模型) max. likelihood (mixed effect model)	0.46	-0.19	0.74	5.30	0.913	1 039.95
层次贝叶斯统计(混合模型) hierarchical Bayesian statistics (mixed effect model)	0.32	0.35	0.58	3.92	0.946		1 021.52

方法method	σ (MAE)	σ (RME)	σ (RMSE)	σ (RMSE%)
极大似然法(基础模型) maximum likelihood (base model)	0.68	1.08	1.17	7.65
贝叶斯统计(基础模型) Bayesian statistic(base model)	0.57	0.79	0.96	6.73
极大似然法(混合模型) maximum likelihood (mixed effect model)	0.61	0.9	1.06	7.59
层次贝叶斯统计(混合模型) hierarchical Bayesian statistics (mixed effect model)	0.56	1.04	1.04	6.81

基于贝叶斯方法的蒙古栎林单木树高-胸径模型

Individual diameter-height model for Mongolian oak forests based on Bayesian method

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 6

参考文献 23

相关文章 1

编辑推荐

Metrics

本文评价

作者

读者

审稿