Modelling Under Risk and Uncertainty: An Introduction to Statistical, Phenomenological and Computational Methods

6.1 Introducing Inverse Techniques

6.1.1 Handling Calibration Data

Recalling the general estimation program introduced in Chapter 2 and sketched in Figure 6.1:

Figure 6.1 Generic context for risk/uncertainty modelling – role of data and expertise.

Data and expertise, denoted by Ξ_n and IK respectively, should best represent the extent of knowledge and lack of knowledge within the combined system and uncertainty model for the subsequent inference of the risk measures. In the simplest situation, covered in Chapter 5, data and expertise enabled the direct estimation of an uncertainty model on the x inputs. In many real-world situations, data and expertise are available on observable variables (the y) that differ from the inputs (the x) required by the phenomenological system models at hand.

For the sake of simplicity, take a scalar example. Consider a simple physical system (e.g. river section, mechanical device) for which both an experimental setting and a corresponding numerical model relate a single observable y (e.g. water level, strain) to a scalar uncertain property x (e.g. friction coefficient, Young modulus) and known environmental conditions d (such as reference flow, temperature, pressure . . . or even time of the experiment, if sedimentary evolution or material ageing is considered, for instance).

(6.1)

(6.2)

where y, y_m and x are scalars, but d can be a vector and the ...