林业科学 ›› 2021, Vol. 57 ›› Issue (3): 51-66.doi: 10.11707/j.1001-7488.20210306
田相林1,2,廖梓延3,4,孙帅超5,薛海连6,王彬7,曹田健1,*
收稿日期:
2019-04-29
出版日期:
2021-03-25
发布日期:
2021-04-07
通讯作者:
曹田健
基金资助:
Xianglin Tian1,2,Ziyan Liao3,4,Shuaichao Sun5,Hailian Xue6,Bin Wang7,Tianjian Cao1,*
Received:
2019-04-29
Online:
2021-03-25
Published:
2021-04-07
Contact:
Tianjian Cao
摘要:
目的: 比较多源数据对林分动态预测的影响,分析模型参数与预测不确定性的变化规律,从准确性和可靠性角度对模型进行评估,获取改进模型的数据需求,为森林调查中的数据收集策略提供建议。方法: 收集秦岭油松林3期调查(1990、2005和2012年)和4种信息类型(临时样地、固定样地、解析木和多源数据)建模数据,设计一组数据信息要求较低的可变密度全林模型,基于贝叶斯信息动态融合框架,分析传统森林调查数据与生长收获模型的关系。利用MCMC抽样技术获得的参数联合后验分布对森林动态模拟的不确定性进行量化:一方面比较相同类型的多期森林调查数据不断对模型进行训练后,模型在参数与预测中的概率分布变化过程;另一方面比较分别采用4种数据类型对模型预测产生的影响。数据与模型更新循环过程以先验信息和后验信息不断相互转化的方法实现,即前一次拟合得到的参数联合后验分布作为下一期数据加入时的先验。不同数据类型整合根据数据自身抽样和观测误差所设计的独立似然结构实现。为避免粗糙数据或异常值对模型产生的影响,描述误差分布的似然函数采用重尾正态分布。观测误差的异方差特性通过迭代中自动调整似然函数的方差控制。结果: 随着新一期调查数据加入,模型参数的边际或联合分布不断发生变化,但概率分布峰度总是逐渐升高,即参数不确定性逐步下降,从而降低林分预测的不确定性。与基于1990年调查数据的模型相比,经过2005和2012年数据校正后模型在成过熟林阶段的不确定性下降最为明显,同时树高生长极大值的参数也更高。不同数据类型在模型预测中的差异反映出不同调查方法本身的缺陷和优势,解析木数据倾向于在成过熟林阶段预测出更高的树高生长;固定样地和临时样地数据在林分平均高和平均胸径模拟中表现相似,但由于抽样方法和数据量等因素区别,导致其在林分断面积模拟中呈现明显差异。基于循环更新或多源数据的模型呈现出最稳定的预测结果。结论: 在生长收获模型构建中,不同类型森林调查数据会产生不同预测结果,不同数据信息特性也会对预测的不确定性产生规律性影响。以概率分布呈现信息的贝叶斯方法,既可反映模型的精准程度,又能解释数据信息中存在的缺陷。本研究以全林模型更新为例,展示了该方法不断循环、更新、融合的数据-模型逻辑框架,是架构生长收获模型与数据桥梁的有力工具。
中图分类号:
田相林,廖梓延,孙帅超,薛海连,王彬,曹田健. 多源数据对林分动态预测的影响及不确定性分析[J]. 林业科学, 2021, 57(3): 51-66.
Xianglin Tian,Ziyan Liao,Shuaichao Sun,Hailian Xue,Bin Wang,Tianjian Cao. Impacts of Multiple Source Data on Forest Forecasting and Uncertainty Propagation[J]. Scientia Silvae Sinicae, 2021, 57(3): 51-66.
表1
用于模型循环更新测试的3期角规样地调查数据"
项目Item | 1990 | 2005 | 2012 | |
样地数量Sample size | 58 | 68 | 45 | |
林分年龄Stand age/a | 最小值Min. | 15 | 25 | 30 |
平均值Mean | 28 | 50 | 58 | |
最大值Max. | 60 | 81 | 87 | |
林分高Stand height/m | 最小值Min. | 5.0 | 8.0 | 8.2 |
平均值Mean | 10.4 | 14.8 | 16.3 | |
最大值Max. | 16.0 | 25.0 | 21.0 | |
林分平均胸径Stand mean DBH/cm | 最小值Min. | 8.0 | 12.0 | 17.1 |
平均值Mean | 17.6 | 22.5 | 26.1 | |
最大值Max. | 44.0 | 33.0 | 35.4 | |
林分密度Stand density/(trees·hm-2) | 最小值Min. | 182 | 151 | 229 |
平均值Mean | 874 | 570 | 523 | |
最大值Max. | 2 355 | 1 557 | 1 006 |
表2
模型构建中比较的3种数据类型"
数据类型 Type of data | 角规临时样地 Temporary plot(TP) | 矩形固定样地 Permanent plot(PP) | 解析木 Stem analysis(SA) | |
调查年份Investigation year | 1990, 2005, 2012—2015 | 2012—2015 | 1980, 2003 | |
样地数量Sample size | 215 | 22 | 11 | |
林分年龄Stand age/a | 最小值Min. | 15 | 20 | |
平均值Mean | 46 | 35 | ||
最大值Max. | 87 | 68 | ||
林分高Stand height/m | 最小值Min. | 5.0 | 8.6 | |
平均值Mean | 13.4 | 12.5 | ||
最大值Max. | 25.0 | 20.4 | ||
林分平均胸径Stand mean DBH/cm | 最小值Min. | 8.0 | 12.9 | |
平均值Mean | 22.0 | 17.4 | ||
最大值Max. | 44.0 | 24.8 | ||
林分密度Stand density/(trees·hm-2) | 最小值Min. | 151 | 600 | |
平均值Mean | 628 | 1 595 | ||
最大值Max. | 2 355 | 3 123 |
表3
参数循环更新过程中后验概率密度分布的变化①"
参数 Parameter | 基于1990年数据的首次拟合 1990 (initial fitting) | 基于2005年数据的一次校正 2005 (calibrated once) | 基于2012年数据的二次校正 2012 (calibrated twice) | ||||||||
均值Mean | 标准差SD | 最大后验MAP | 均值Mean | 标准差SD | 最大后验MAP | 均值Mean | 标准差SD | 最大后验MAP | |||
b1 | 19.145 8 | 1.164 9 | 18.311 0 | 21.358 6 | 1.087 5 | 21.114 1 | 22.445 6 | 0.612 4 | 22.830 4 | ||
b2 | 17.457 3 | 1.595 0 | 16.910 0 | 19.310 2 | 1.678 7 | 18.914 0 | 21.752 9 | 1.114 0 | 22.417 9 | ||
c1 | 12.188 3 | 1.819 9 | 10.221 0 | 25.654 9 | 2.046 0 | 26.918 4 | 28.301 6 | 1.267 2 | 29.871 8 | ||
c2 | 0.323 3 | 0.063 7 | 0.387 5 | 0.039 3 | 0.031 6 | 0.019 2 | 0.027 3 | 0.019 7 | 0.004 1 | ||
c3 | 5.252 9 | 1.366 3 | 5.404 5 | 3.590 3 | 0.578 2 | 3.672 5 | 4.862 0 | 0.475 7 | 4.774 3 | ||
c4 | 1.371 2 | 0.196 7 | 1.291 6 | 2.375 1 | 0.169 2 | 2.397 2 | 2.205 6 | 0.105 6 | 2.215 8 | ||
d1 | 22.197 5 | 2.126 8 | 20.666 8 | 32.189 7 | 2.675 2 | 35.328 9 | 37.048 7 | 1.665 5 | 36.943 9 | ||
d2 | 0.156 3 | 0.057 0 | 0.163 3 | 0.033 3 | 0.029 8 | 0.003 2 | 0.017 8 | 0.016 4 | 0.015 2 | ||
d3 | 19.043 4 | 2.854 3 | 17.468 1 | 20.178 5 | 1.697 0 | 20.260 1 | 23.997 3 | 1.410 6 | 24.213 0 | ||
d4 | 0.057 6 | 0.045 5 | 0.010 2 | 0.028 2 | 0.026 1 | 0.002 0 | 0.092 4 | 0.048 2 | 0.160 6 |
表4
基于多源数据的参数后验概率分布"
参数 Parameter | 临时样地TP | 固定样地PP | 解析木SA | 多源数据MSD | |||||||||||
均值 Mean | 标准差 SD | 最大后验 MAP | 均值 Mean | 标准差 SD | 最大后验 MAP | 均值 Mean | 标准差 SD | 最大后验 MAP | 均值 Mean | 标准差 SD | 最大后验 MAP | ||||
b1 | 22.445 6 | 0.612 4 | 22.830 4 | 20.777 6 | 1.263 4 | 19.888 2 | 29.766 9 | 0.217 6 | 29.996 2 | 22.529 9 | 0.565 0 | 22.637 6 | |||
b2 | 21.752 9 | 1.114 0 | 22.417 9 | 17.025 6 | 1.511 7 | 16.254 4 | 20.868 3 | 0.601 0 | 21.089 8 | 20.218 4 | 0.966 3 | 20.355 2 | |||
c1 | 28.301 6 | 1.267 2 | 29.871 8 | 21.259 3 | 5.527 1 | 29.477 4 | 28.804 5 | 1.074 6 | 29.919 6 | ||||||
c2 | 0.027 3 | 0.019 7 | 0.004 1 | 0.206 4 | 0.117 9 | 0.087 2 | 0.023 7 | 0.016 8 | 0.000 7 | ||||||
c3 | 4.862 0 | 0.475 7 | 4.774 3 | 9.809 2 | 2.063 2 | 11.730 7 | 5.231 8 | 0.494 9 | 4.779 6 | ||||||
c4 | 2.205 6 | 0.105 6 | 2.215 8 | 0.583 9 | 0.533 7 | 0.285 3 | 2.111 3 | 0.104 6 | 2.205 6 | ||||||
d1 | 37.048 7 | 1.665 5 | 36.943 9 | 23.669 3 | 2.034 8 | 21.567 1 | 36.186 8 | 1.547 0 | 35.756 8 | ||||||
d2 | 0.017 8 | 0.016 4 | 0.015 2 | 0.052 0 | 0.032 1 | 0.068 5 | 0.015 2 | 0.014 5 | 0.019 9 | ||||||
d3 | 23.997 3 | 1.410 6 | 24.213 0 | 13.876 3 | 1.172 4 | 12.707 9 | 22.690 0 | 1.040 9 | 23.000 6 | ||||||
d4 | 0.092 4 | 0.048 2 | 0.160 6 | 0.070 4 | 0.061 2 | 0.049 5 | 0.070 0 | 0.037 1 | 0.090 0 |
表5
基于方差的不确定性量化分解"
参数 Parameter | 模型参数对各输出变量的Sobol总效应指数Sobol’s total-effect indices of parameter to the output | |||
林分平均高 Stand mean height | 林分断面积 Stand basal area | 林分平均胸径 Stand mean DBH | 林分密度 Stand density | |
b1 | 0.94 | — | — | — |
b2 | 0.89 | — | — | — |
c1 | — | 0.93 | — | 0.90 |
c2 | — | 0.99 | — | 0.96 |
c3 | — | 1.00 | — | 0.98 |
c4 | — | 0.83 | — | 0.75 |
d1 | — | — | 0.80 | 0.95 |
d2 | — | — | 0.72 | 0.90 |
d3 | — | — | 0.78 | 0.83 |
d4 | — | — | 0.36 | 0.46 |
符利勇, 雷渊才, 孙伟, 等. 不同林分起源的相容性生物量模型构建. 生态学报, 2014, 34 (6): 1461- 1470. | |
Fu L Y , Lei Y C , Sun W , et al. Development of compatible biomass models for trees from defferent stand origin. Acta Ecologica Sinica, 2014, 34 (6): 1461- 1470. | |
郭小阳, 吴恒, 田相林, 等. 基于优势高模型分析多源数据对立地质量评价的影响. 西北林学院学报, 2017, 32 (6): 184- 189.
doi: 10.3969/j.issn.1001-7461.2017.06.28 |
|
Guo X Y , Wu H , Tian X L , et al. Effect fo multiple source data on site evaluation based on dominant height modeling. Journal of Northwest Forest University, 2017, 32 (6): 184- 189.
doi: 10.3969/j.issn.1001-7461.2017.06.28 |
|
洪玲霞. 由全林整体生长模型推导林分密度控制图的方法. 林业科学研究, 1993, 6 (5): 510- 516. | |
Hong L X . An approach to derive stand density control chart from the integrated stand growth model. Forest Research, 1993, 6 (5): 510- 516. | |
洪玲霞, 雷相东, 李永慈. 蒙古栎林全林整体生长模型及其应用. 林业科学研究, 2012, 25 (2): 201- 206.
doi: 10.3969/j.issn.1001-1498.2012.02.015 |
|
Hong L X , Lei X D , Li Y C . Integrated stand growth model of Mongolian oak and it's application. Forest Research, 2012, 25 (2): 201- 206.
doi: 10.3969/j.issn.1001-1498.2012.02.015 |
|
李希菲, 唐守正, 王松林. 大岗山实验局杉木人工林可变密度收获表的编制. 林业科学研究, 1988, 1 (4): 382- 389. | |
Li X F , Tang S Z , Wang S L . The establishment of variable density yield table for Chinese fir plantation in Dagangshan experiment bureau. Forest Research, 1988, 1 (4): 382- 389. | |
李悦黎, 杜纪山. 火地塘教学实验林场森林资源的数据分析及经营对策. 西北林学院学报, 1993, 8 (3): 53- 58. | |
Li Y L , Du J S . Analysis and management strategy of forest resources of Huoditang teaching and experimental forest farm. Jorunal of Northest Forestry College, 1993, 8 (3): 53- 58. | |
唐守正. 广西大青山马尾松全林整体生长模型及其应用. 林业科学研究, 1991, 4 (增): 8- 13. | |
Tang S Z . Integrated stand growth model of massion pine in Daqingshan Mountain, Guangxi Province. Forest Research, 1991, 4 (Supp.): 8- 13. | |
唐守正. 同龄纯林自然稀疏规律的研究. 林业科学, 1993, 29 (3): 234- 241.
doi: 10.3321/j.issn:1001-7488.1993.03.005 |
|
Tang S Z . The research of self-thinning law for even-aged pure stands. Scientia Silvae Sinicae, 1993, 29 (3): 234- 241.
doi: 10.3321/j.issn:1001-7488.1993.03.005 |
|
唐守正, 杜纪山. 利用树冠竞争因子确定同龄间伐林分的断面积生长过程. 林业科学, 1999, 35 (6): 35- 41.
doi: 10.3321/j.issn:1001-7488.1999.06.005 |
|
Tang S Z , Du J S . Determining basal area growth process of thinned even-aged stands by crown competition factor. Scientia Silvae Sinicae, 1999, 35 (6): 35- 41.
doi: 10.3321/j.issn:1001-7488.1999.06.005 |
|
唐守正, 李希菲. 用全林整体模型计算林分纯生长量的方法及精度分析. 林业科学研究, 1995, 8 (5): 471- 476. | |
Tang S Z , Li X F . Precision Analysis on growth rates estimated by integrated whole stand growth and yield model. Forest Research, 1995, 8 (5): 471- 476. | |
唐守正, 李勇. 一种多元非线性度量误差模型的参数估计及算法. 生物数学学报, 1996, 11 (1): 23- 27. | |
Tang S Z , Li Y . An algorithm for estimating multivariate non-linear error-in-measure models. Journal of Biommethmatics, 1996, 11 (1): 23- 27. | |
唐守正, 张淑梅. 度量误差模型及其应用. 生物数学学报, 1998, 13 (2): 161- 166.
doi: 10.3969/j.issn.1001-9626.1998.02.008 |
|
Tang S Z , Zhang S M . Measurement error models and their applications. Journal of Biommethmatics, 1998, 13 (2): 161- 166.
doi: 10.3969/j.issn.1001-9626.1998.02.008 |
|
吴恒, 党坤良, 田相林, 等. 秦岭林区天然次生林与人工林立地质量评价. 林业科学, 2015, 51 (4): 78- 88. | |
Wu H , Dang K L , Tian X L , et al. Evaluating site quality for secondary forests and plantation in Qinling Mountains. Scientia Silvae Sinicae, 2015, 51 (4): 78- 88. | |
张少昂. 兴安落叶松天然林林分生长模型和可变密度收获表的研究. 东北林业大学学报, 1986, 14 (3): 17- 25. | |
Zhang S A . Study on natural Dahurian larch stand growth model and variable density yield table. Journal of Northeast Forestry University, 1986, 14 (3): 17- 25. | |
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. 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. Scientia Sivae Sinicae, 2014, 50 (3): 69- 75. | |
Ando T , Zellner A . Hierarchical Bayesian analysis of the seemingly unrelated regression and simultaneous equations models using a combination of direct Monte Carlo and importance sampling techniques. Bayesian Analysis, 2010, 5 (1): 65- 95. | |
Berger J O . Bayesian analysis: a look at today and thoughts of tomorrow. Journal of the American Statistical Association, 2000, 95 (452): 1269- 1276. | |
Bijleveld C C J H , van der Kamp L J T . Longitudinal data analysis: designs, models and methods. SAGE Publications Ltd, 1998. | |
Bontemps J D , Hervé J C , Dhôte J F . Long-tern changes in forest productivity: a consistent assessment in even-aged stands. Forest Science, 2009, 55 (6): 549- 564. | |
Brooks S , Gelman A . General methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics, 1998, 7, 434- 455. | |
Bullock B P , Boone E L . Deriving tree diameter distributions using Bayesian model averaging. Forest Ecology and Management, 2007, 242 (2): 127- 132. | |
Cariboni J , Gatelli D , Liska R , et al. The role of sensitivity analysis in ecological Modelling. Ecological Modelling, 2007, 203 (1/2): 167- 182. | |
Clark J S . Models for ecological data: an introduction. New Jersey: Princeton University Press, 2007. | |
Clark J S , Wolosin M , Dietze M , et al. Tree growth inference and prediction from diameter censuses and ring widths. Ecological Applications, 2007, 17 (7): 1942- 1953.
doi: 10.1890/06-1039.1 |
|
Dietze M C . Ecological forecasting. Princeton University Press, 2017. | |
Dietze M C , Wolosin M S , Clark J S . Capturing diversity and interspecific variability in allometries: a hierarchical approach. Forest Ecology and Management, 2008, 256 (11): 1939- 1948.
doi: 10.1016/j.foreco.2008.07.034 |
|
Efron B . Computers and the theory of statistics: thinking the unthinkable. SIAM Review, 1979, 21 (4): 460- 480.
doi: 10.1137/1021092 |
|
Fox T R . Sustained productivity in intensively managed forest plantations. Forest Ecology and Management, 2000, 138 (1/3): 187- 202. | |
Gelfand A E , Smith A F . Sampling-based approaches to calculating marginal densities. Journal of the American statistical association, 1990, 85 (410): 398- 409.
doi: 10.1080/01621459.1990.10476213 |
|
Gelman A , Hill J . Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, 2007. | |
Gelman A, Rubin D. 1992. Inference from iterative simulation using multiple sequences. Technical Report No. 307. vol 7. | |
Gilks W R , Richardson S , Spiegelhalter D J . Markov Chain Monte Carlo in practice. London: Chapman and Hall, 1996. | |
Green E J , Strawderman W E . A Bayesian growth and yield model for slash pine plantations. Journal of Applied Statistics, 1996, 23 (2/3): 285- 300. | |
Hann D L, Hanus M. 2002. Enhanced diameter-growth-rate equations for undamaged and damaged trees in southwest Oregon. Research Contribution 39. Oregon State University, Forest Research Laboratory, Corvallis O R. | |
Hartig F , Dyke J , Hickler T , et al. Connecting dynamic vegetation models to data-an inverse perspective. Journal of Biogeography, 2012, 39 (12): 2240- 2252.
doi: 10.1111/j.1365-2699.2012.02745.x |
|
Hartig F, Minunno F, Paul S. 2019. BayesianTools: general-purpose MCMC and SMC samplers and tools for Bayesian statistics. R package version 0. 1. 7. https://CRAN.R-project.org/package=BayesianTools. | |
Hastings W K . Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 1970, 57 (1): 97- 109.
doi: 10.1093/biomet/57.1.97 |
|
Iooss B, Da Veiga S, Janon A, et al. 2020. sensitivity: Global Sensitivity Analysis of Model Outputs. R package version 1. 19. 0. https://CRAN.R-project.org/package=sensitivity. | |
Kangas A , Maltamo M . Forest inventory: methodology and applications. Netherlands: Springer Science & Business Media, 2006. | |
LeBauer D S , Wang D , Richter K T , et al. Facilitating feedbacks between field measurements and ecosystem models. Ecological Monographs, 2013, 83 (2): 133- 154.
doi: 10.1890/12-0137.1 |
|
Li R , Stewart B , Weiskittel A . A Bayesian approach for modelling non-linear longitudinal/hierarchical data with random effects in forestry. Forestry, 2011, 85 (1): 17- 25. | |
Marler R T , Arora J S . The weighted sum method for multi-objective optimization: new insights. Structural Multidisciplinary Optimization, 2010, 41 (6): 853- 862.
doi: 10.1007/s00158-009-0460-7 |
|
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. Canadian Journal of Forest Research, 2009, 39 (9): 1677- 1687.
doi: 10.1139/X09-083 |
|
Metropolis N , Rosenbluth A W , Rosenbluth M N , et al. Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 1953, 21 (6): 1087- 1092.
doi: 10.1063/1.1699114 |
|
Monserud R A , Rehfeldt G E . Genetic and environmental components of variation of site index in inland Douglas-fir. Forest Science, 1990, 36 (1): 1- 9. | |
Pretzsch H . Forest dynamics, growth, and yield. Heidelberg: Springer, 2010. | |
Radtke P J , Robinson A P . A Bayesian strategy for combining predictions from empirical and process-based models. Ecological Modelling, 2006, 190 (3): 287- 298. | |
Raulier F , Lambert M C , Pothier D , et al. Impact of dominant tree dynamics on site index curves. Forest Ecology and Management, 2003, 184 (1/3): 65- 78. | |
Reineke L H . Perfecting a stand-density index for even-aged forests. Journal of Agricultural Research, 1933, 46 (7): 627- 638. | |
Saltelli A , Ratto M , Andres T , et al. Global sensitivity analysis: the primer. John Wiley & Sons, 2008, | |
Schroth G , Sinclair F . Trees, crops and soil fertility-concepts and research methods. Wallingford: CABI pubishing, 2003. | |
Schumacher F . A new growth curve and its application to timber yield studies. Journal of Forestry, 1939, 37 (33): 819- 820. | |
Sivia D , Skilling J . Data analysis: a Bayesian tutorial. UK: Oxford University Press, 2006. | |
Skovsgaard J P , Vanclay J K . Forest site productivity: a review of the evolution of dendrometric concepts for even-aged stands. Forestry, 2008, 81 (1): 13- 31.
doi: 10.1093/forestry/cpm041 |
|
Van Laar A , Akça A . Forest mensuration. Netherlands: Springer Science & Business Media, 2007. | |
Van Oijen M . Bayesian methods for quantifying and reducing uncertainty and error in forest models. Current Forestry Reports, 2017, 3 (4): 269- 280.
doi: 10.1007/s40725-017-0069-9 |
|
Van Oijen M , Rougier J , Smith R . Bayesian calibration of process-based forest models: bridging the gap between models and data. Tree Physiology, 2005, 25 (7): 915- 927.
doi: 10.1093/treephys/25.7.915 |
|
Ware J , Liang K . The design and analysis of longitudinal studies: a historical perspective. Advances in Biometry, 1996, 339- 362. | |
Weiskittel A R , Hann D W , Kershaw Jr J A , et al. Forest growth and yield modeling. John Wiley & Sons, 2011, | |
West M , Harrison J . Bayesian forecasting and dynamic models. New York: Springer, 1997. | |
Zapata-Cuartas M , Sierra C A , Alleman L . Probability distribution of allometric coefficients and Bayesian estimation of aboveground tree biomass. Forest Ecology and Management, 2012, 277, 173- 179.
doi: 10.1016/j.foreco.2012.04.030 |
|
Zhang X , Duan A , Zhang J . Tree biomass estimation of Chinese fir (Cunninghamia lanceolata) based on bayesian method. PloS One, 2013, 8 (11): e79868..
doi: 10.1371/journal.pone.0079868 |
|
Zellner A . An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. Journal of the American statistical Association, 1962, 57 (298): 348- 368.
doi: 10.1080/01621459.1962.10480664 |
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