A large proportion of undesirable events like earthquakes, floods, tornados occur in zones where these events are frequent. However, a significant number of such events occur in other zones, where such events are rare. For example, while most major earthquakes occur in a vicinity of major faults, i.e., on the border between two tectonic plates, some strong earthquakes also occur inside plates. We want to mitigate all undesirable events, but our resources are limited. So, to allocate these resources, we need to decide which ones are more important. For this decision, a natural idea is to use the product of the probability of the undesirable event and possible damage caused by this event. A natural way to estimate probability is to use the frequency of such events in the past. This works well for high-probability events like earthquakes in a seismic zone near a fault. However, for low-probability high-impact event the frequency is small and, as a result, the actual probability may be very different from the observed frequency. In this paper, we show how to take this difference between frequency and probability into account. We also show that if we do take this difference into account, then low-probability high-impact events turn out to be even more important than it is usually assumed.
Technical Report: UTEP-CS-23-15