Ways to Understand and Approach Rare Events

摘要

As a matter of fact, avoiding unexpected events with an undesired outcome is an element of survival strategies. Such events are encountered unexpectedly mainly because they occur rarely. Both, safety and security measures are the main pillars to prevent them by appropriate inspections. Common tools in both areas e.g. are radiological technologies enabling an insight into objects to detect suspicious features without even touching them. Since any of these measures is linked to efforts, costs or even obstructions of ongoing processes, it needs a rationale to invest into an appropriate activity. A putative objection to take action in this direction always could be the question "when and how often it could happen". This gave rise to find approaches how to define "rare events" and how to deal with them. Since they entail both, the frequency of occurrence and the unpleasantness of the possible outcome make them to have something in common with the definition of risk: a combination of the probability of occurrence of harm and the severity of that harm. Tackling putative consequences is one side of the coin whereas understanding the rareness of an event is the other, an aspect that worries but not always fully understood. As a first step in approaching the subject "rare events", the putative occurrence rate is considered in terms of probability distribution functions or their cumulative ones, resp. The problems of estimating an incidence of such an event will be tackled subsequently with the problem of assessing the reliability of diagnostic measures. Any numeric approach of dealing with rare events inevitably remains an ill defined or "ill-posed" problem that needs additional information for a reasonably satisfying solution. Ways to ease this situation can be found in utilizing additional information, also commonly called prior knowledge, that might be introduced via the Bayesian inference or by regularization algorithms. Simplified models will demonstrate how to apply such tools. As a consequence, there are ways helping to avoid unexpected bad "surprises" by taking adequate measures in due time upon the correct perception of certain indications.