  Rare events can potentially occur in many applications. When manifested as
opportunities to be exploited, risks to be ameliorated, or certain features to
be extracted, such events become of paramount significance. Due to their
sporadic nature, the information-bearing signals associated with rare events
often lie in a large set of irrelevant signals and are not easily accessible.
This paper provides a statistical framework for detecting such events so that
an optimal balance between detection reliability and agility, as two opposing
performance measures, is established. The core component of this framework is a
sampling procedure that adaptively and quickly focuses the
information-gathering resources on the segments of the dataset that bear the
information pertinent to the rare events. Particular focus is placed on
Gaussian signals with the aim of detecting signals with rare mean and variance
values.
