## Statistical calibration of processbased simulation models

Since the introduction of modern, high-speed computers, there has been a trend among ecologists to develop complex simulation models of ecosystems. The objective of these models is to provide a realistic, mechanistically detailed representation of the modeled system and not necessarily to serve as an elegant conceptualization. While in theory, models that are built from first principles of physics, chemistry, and biology do not need to be calibrated to data, the reality is that 'tweaking' of model parameters is usually necessary to produce good simulations. This is also true for simpler models, such as population simulations.

The process of calibrating process-based models can be formalized by viewing the problem as a large, nonlinear regression analysis. If a form for the model error term can be assumed and sufficient data are available, then optimization algorithms can be used to estimate the 'best-fitting' parameter values in a manner similar to regression estimation. Predictive error can then be assessed by accounting for both parameter uncertainty and residual error, as described above in the context of simple regression models.

Unfortunately, there are at least two problems with this approach. First, there are rarely enough data available for a particular problem setting to be able to uniquely identify model parameter values from data alone. Second, even if the model could be sufficiently simplified to avoid this problem of 'overparametrization', it is likely that prediction error would be significantly underestimated by regression-based methods. This is because such methods do not account for uncertainty in the model structure itself, which is usually quite large. It is unrealistic to expect that there is a single, 'true' model of a complex ecological system and that the modeler has correctly identified such a model. In reality there are likely to be several models which all approximate the system equally well as far as one can determine from the available data. This situation calls for methods which can deal with multiple models and overparametrized models, such as those described in the next section.

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