Bayesian calibration of process-based forest models: bridging the gap between models and data

被引:253
作者
Van Oijen, M
Rougier, J
Smith, R
机构
[1] CEH Edinburgh, Penicuik EH26 0QB, Midlothian, Scotland
[2] Univ Durham, Durham DH1 3LE, England
关键词
Markov chain Monte Carlo; tree measurement; parameterization; uncertainty;
D O I
10.1093/treephys/25.7.915
中图分类号
S7 [林业];
学科分类号
0829 ; 0907 ;
摘要
Process-based forest models generally have many parameters, multiple outputs of interest and a small underlying empirical database. These characteristics hamper parameterization. Bayesian calibration offers a solution to the calibration problem because it applies to models of any type or size. It provides parameter estimates, with measures of uncertainty and correlation among the parameters. The procedure begins by quantifying the uncertainty about parameter values in the form of a prior probability distribution. Then data on the output variables are used to update the parameter distribution by means of Bayes' Theorem. This yields a posterior calibrated distribution for the parameters, which can be summarized in the form of a mean vector and variance matrix. The predictive uncertainty of the model can be quantified by running it with different parameter settings, sampled from the posterior distribution. In a further step, one may evaluate the posterior probability of the model itself (rather than that of the parameters) and compare that against the probability of other models, to aid in model selection or improvement. Bayesian calibration of process-based models cannot be performed analytically, so the posterior parameter distribution must be approximated in the form of a representative sample of parameter values. This can be achieved by means of Markov Chain Monte Carlo simulation, which is suitable for process-based models because of its simplicity and because it does not require advance knowledge of the shape of the posterior distribution. Despite the suitability of Bayesian calibration, the technique has rarely been used in forestry research. We introduce the method, using the example of a typical forest model. Further, we show that reductions in parameter uncertainty, and thus in output uncertainty, can be effected by increasing the variety of data, increasing the accuracy of measurements and increasing the length of time series.
引用
收藏
页码:915 / 927
页数:13
相关论文
共 40 条
[1]  
[Anonymous], 1988, LECT NOTES STAT
[2]  
[Anonymous], 2012, Probability Theory: The Logic Of Science
[3]  
Bernardo J., 2009, Bayesian theory
[4]   Ecological forecasts: An emerging imperative [J].
Clark, JS ;
Carpenter, SR ;
Barber, M ;
Collins, S ;
Dobson, A ;
Foley, JA ;
Lodge, DM ;
Pascual, M ;
Pielke, R ;
Pizer, W ;
Pringle, C ;
Reid, WV ;
Rose, KA ;
Sala, O ;
Schlesinger, WH ;
Wall, DH ;
Wear, D .
SCIENCE, 2001, 293 (5530) :657-660
[5]   Bayesian forecasting for complex systems using computer simulators [J].
Craig, PS ;
Goldstein, M ;
Rougier, JC ;
Seheult, AH .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2001, 96 (454) :717-729
[6]   Bayesian inference in ecology [J].
Ellison, AM .
ECOLOGY LETTERS, 2004, 7 (06) :509-520
[7]   An introduction to Bayesian inference for ecological research and environmental decision-making [J].
Ellison, AM .
ECOLOGICAL APPLICATIONS, 1996, 6 (04) :1036-1046
[8]  
GARDNER RH, 1990, PROCESS MODELING OF FOREST GROWTH RESPONSES TO ENVIRONMENTAL STRESS, P208
[9]   A Bayesian approach for estimating the parameters of a forest process model based on long-term growth data [J].
Gertner, GZ ;
Fang, SF ;
Skovsgaard, JP .
ECOLOGICAL MODELLING, 1999, 119 (2-3) :249-265
[10]   Communicating complexity and uncertainty in decision making contexts: Bayesian approaches to forest research [J].
Ghazoul, J ;
McAllister, M .
INTERNATIONAL FORESTRY REVIEW, 2003, 5 (01) :9-19