Improving the Use of Data for Quantifying Uncertainty in Parameters and Predictions of Forest Dynamic Models by Bayesian Approach

Improving the Use of Data for Quantifying Uncertainty in Parameters and Predictions of Forest Dynamic Models by Bayesian Approach

Ecological models may include components which are stochastic: climaticparameters, spatial structure and so on. Therefore, the model outputs possess inevitableuncertainties. Moreover, the output uncertainty depends on variability and/or uncertaintyof parameters and initial values. Uncertainty analysis which studies how input variabilityinfluences a variability of output is an important part of a model building allowingseparating different sources of uncertainties. Another task, which is associated withhighly structured multiparameterized model is sensitivity analysis, goal of which is tocharacterize how the model outputs respond to changes in the inputs. Both uncertaintyand sensitivity analysis can be conducted by means of the Monte Carlo procedure. To usea model in specific context it may be necessary to calibrate the model by using someobserved data. Calibration is a reduction of uncertainty of input parameters and it is a keystage of a model building. An effective approach based on Bayesian estimation wasproposed recently [1,2] allowing one to incorporate a prior knowledge of parametervariability. There is a certain difficulty when applying the Bayesian calibration forparameters of highly complicate models, which is a case of spatially explicit individualbasedmodels [3]. For such models the likelihood, connecting data (output) andparameters (input) in probabilistic form, is either impossible or computationallyprohibitive to obtain. Recently, there was proposed a Markov chain Monte Carlo methodfor generating samples from a posterior distribution without the use of the likelihood [4].We discuss uncertainty and sensitive analysis and Bayesian calibration issues by exampleof a model of growth and cycling of elements in boreal forest ecosystems EFIMOD [3].1. Gertner, G.Z., Fang, S., Skovsgaard, J.P. (1999). Ecological Modelling, 119: 249-265.2. Van Oijen, M., Rougier, J. and Smith, R. (2005). Tree Physiology 25: 915-927.3. Komarov, A., Chertov, O., et al., (2003). Ecological Modelling, 170: 373-3924. Marjoram, P. et al., (2003). Proc. Natl. Acad. Sci. USA, 100: 15324-15328.