Info-gap decision theory

Info-gap decision theory is a non-probabilistic decision theory that seeks to optimize robustness to failure – or opportuneness for windfall – under severe uncertainty, in particular applying sensitivity analysis of the stability radius type to perturbations in the value of a given estimate of the parameter of interest. It has some connections with Wald's maximin model; some authors distinguish them, others consider them instances of the same principle.

It has been developed since the 1980s by Yakov Ben-Haim, and has found many applications and described as a theory for decision-making under "severe uncertainty". It has been criticized as unsuited for this purpose, and alternatives proposed, including such classical approaches as robust optimization.

Info-gap is a decision theory: it seeks to assist in decision-making under uncertainty. It does this by using 3 models, each of which builds on the last. One begins with a model for the situation, where some parameter or parameters are unknown. One then takes an estimate for the parameter, which is assumed to be substantially wrong, and one analyzes how sensitive the outcomes under the model are to the error in this estimate.

Info-gap theory models uncertainty ${\displaystyle \alpha }$ (the horizon of uncertainty) as nested subsets ${\displaystyle {\mathcal {U}}(\alpha ,{\tilde {u}})}$ around a point estimate ${\displaystyle {\tilde {u}}}$ of a parameter: with no uncertainty, the estimate is correct, and as uncertainty increases, the subset grows, in general without bound. The subsets quantify uncertainty – the horizon of uncertainty measures the "distance" between an estimate and a possibility – providing an intermediate measure between a single point (the point estimate) and the universe of all possibilities, and giving a measure for sensitivity analysis: how uncertain can an estimate be and a decision (based on this incorrect estimate) still yield an acceptable outcome – what is the margin of error?

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