In the Validation of complex computer/math models the question of interest is to what extent the model adequately represents reality, and for what
ranges of the input parameters. We address these questions within the Bayesian statistical methodology. This allows efficient handling (and
propagation) of all uncertainties (errors)present in the problem.
The primary goal of Validation is often to provide model predictions and associated predictive errors in untested situations. However, a necessary byproduct is the solving of the inverse problem, that is, learning about
the input parameters given the output from the model and the field data.
Bayesian methodology is especially well suited for these purposes.
Bayesian solutions for complicated models usually involve MC or MCMC methods, and hence they require thousands of model runs. If the model is
expensive (slow) to run, it has to be approximated in some fashion. We have successfully used response surface approximations to the models for the purpose of running the MCMC. These purely statistical approaches use the model as "black boxes", and are thus most appropriate when the code can not be accessed and/or manipulated.
The methodology will be exemplified in two real applications.
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