Info-gap value of information in model updating

Information is the complement of uncertainty, so model updating-which is a process of acquiring information-entails the reduction of uncertainty. We concentrate on severe uncertainty quantified with information-gap uncertainty models, so updating focusses on the improvement of info-gap models of uncertainty. Our main effort is to show how model updating can be evaluated in terms of the performance of the system itself. The central tool in this evaluation is the robustness function, whose value expresses the greatest level of info-gap uncertainty consistent with successful performance. A theorem establishes an irrevocable trade-off between robustness and reward (with fixed information). The demand value of an increment of information is the increment of improvement in performance (or reward) which the system can achieve without suffering a loss of robustness, in exchange for applying the information. The demand value of an increment of information is evaluated by comparing the robustness trade-off curves before and after updating. The second theorem introduces an idea of the 'informativeness' of an info-gap model of uncertainty in terms of set inclusion: an uncertainty model is informative to the degree that it more tightly delimits the range of unknown variation. The main implication of the theorem is that information is universally valuable only when it satisfies the set-inclusion criterion. We consider three examples which illustrate the evaluation of the demand value of information. The importance of establishing the comparability of the info-gap models is stressed. It is explained that the demand value can be evaluated either as an a priori estimate of the potential value of information which is not yet in hand, or as an a posteriori assessment of information which has been acquired. (C) 2001 Academic Press.