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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.