Chapter 6
Combined Model Estimation Through Inverse Techniques
The general modelling framework (Chapter 2) has shown the need for estimating the uncertainty model as a prior step before the computation of risk measures and sensitivity and importance indices (Chapter 7) or optimisation in support of decision-making (Chapter 8). Following upon the previous chapter where direct estimation was discussed, this chapter develops the estimation theory in the case where available modelling information may be indirect, in the sense that the system model needs some form of inversion in order to retrieve the useful variables. In other words, the inference of uncertainty pdf concerns the hidden input variables of large physical models for which only the outputs are observable. It will be seen that this also embraces the essential issues of the calibration and validation of system models as against data and expertise, enabling thereby some form of control of model uncertainty. Inverse probabilistic problems include data assimilation or regression settings for calibration and full probabilistic inversion so as to identify the intrinsic variability of inputs, a spectrum of quite different motivation-based techniques for which clear distinctions will be made hereafter and challenging research algorithms reviewed. One of the big issues in practice is to limit to a reasonable level the number of (usually large CPU-consuming) physical model runs inside the inverse algorithms.
