Example 3: Rare events

Terms such as rare events, extreme events, surprises, catastrophes are often used to refer to events that deviate significantly (e.g. in magnitude) from the “expected”, “anticipated”, “estimated”, “nominal” event under consideration (e.g. flood level).

And it is precisely because such events are rare that it prove so difficult to handle them by means of conventional statistical/probabilistic methods. Because, even if models to describe them are available, the data to determine the values of the models’ parameters is lacking.

That said, a particularly interesting point is raised by the following question:

In a schematic description of an event space, where should rare events be located in relation to the “best estimate” of the event? Would rare events be located near the best estimate, or at a significant distance from it?

For instance, suppose that the “event” under consideration is the “annual rainfall (mm) in Melbourne (Australia) in 2012”. What would be a rare event in this case, given that the average annual rainfall in Melbourne (Australia) is about 650mm ? Would 620mm count as a rare event in this case?

We raise this issue to point out that voodoo methodolgies can be rather lax in their approach to rare events, extreme events, etc. For instance, info-gap decision theory seems to have no qualms whatsoever about placing rare events, extreme events, surprises, catastrophes, etc. in close proximity to the “best estimate”. To see that this is indeed the case, consider the following graphic depiction of the situation:


Here the large rectangle represents the uncertainty space, the small black dot represents the estimate, and the white area around the estimate represents the neighborhood of the estimate on which info-gap’s robustness analysis is conducted.

The conclusion to be drawn then is this: as info-gap decision theory claims to provide a reliable methodology for dealing with surprises, catastrophes and the like, and as this methodology prescribes an analysis that is confined to the neighborhood around the estimate it follows that, according to info-gap decision theory, surprises are in close proximity of the estimate.