Why Rare, High-Impact Risks Resist Probability Estimation

Summary

The document considers how to estimate the likelihood of low-frequency, high-impact operational risk scenarios. The questioner proposes fitting distributions for event frequency and severity as a possible starting point. The reply cautions that selecting a suitable distribution for rare events is difficult and does not fit neatly into standard statistical inference.

Instead of supplying a probability estimate or a fitted model, the answer points to a heuristic for detecting model error and fragility that does not rely on assigning probabilities. It frames rare-event analysis as limited by the difficulty of inferring future extremes from observed data. The discussion is conceptual and offers no worked example, empirical evidence, or operational procedure for applying the suggested heuristic, so it is not a complete estimation method.

Key ideas

• Rare, severe scenarios are difficult to estimate from observed data.
• Modeling frequency and severity distributions is suggested as one possible approach.
• The reply highlights the limits of classical statistical inference for rare events.
• A probability-free heuristic for detecting model error is mentioned, but not explained.

Tags

# How to estimate the probability of a scenario in general


# How to estimate the probability of a scenario in general












For my finance lecture we are currently on the topic of operation risk.

Scenarios play a vital role in the estimation of low frequency (or probability), high impact (or severity) events. How could you estimate the probability of a scenario?

This question is 2 marks, but would a step in the right direction be finding an appropriate distribution for frequency and severity of events.

## Answer by Zach (score 1)

https://quant.stackexchange.com/a/30435

This is a particularly fascinating area of inference, at least in my opinion. While you are asking for an estimation of the probability of an unlikely event, I'll instead offer a paper that presents a heuristic for detection of model error. It is explicitly probability free.

Mathematical Definition, Mapping, and Detection of (Anti)Fragility

Taleb has spent the majority of his professional life dealing with so-called "Black Swan Events" (a term he popularized with his book "The Black Swan").

To the point, finding an appropriate distribution of low frequency events is a particularly troublesome task that does not fit nicely into classical statistical inference. Those events go to the heart of Hume's problem of induction, a topic that Taleb seems to have devoted his professional life to.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.