Pattern Recognition (PR) in its standard form, which involves training and testing classifiers on a representative set of data drawn from a domain of interest, has been applied to automate an immense number of classification tasks. More recently, a challenging set of so-called ``one-class'' classification problems have been identified and explored. In this thesis, we introduce a further challenging class of PR problems, involving the recognition of Stochastically Episodic (SE) events, and present a first attempt at classifying them within their characteristic fields of background noise. More specifically, this class of problems is characterized by the presence of an overwhelming number of background measurements, which are acquired in the form of a time-series. The time-series is, however, interwoven with a minute number of random (in time, space and magnitude) SE events, which are deemed to be of considerable interest and require classification. The rarity and random nature of the SE events, along with their presence within a time-series of noise-like measurements, renders the learning of their corresponding distribution extremely difficult, if not entirely impossible. By extension, the classification of the SE events is an extremely interesting and ambitious undertaking. Since the acquisition of a sufficient number of SE events is, by definition, unachievable, we propose a flexible framework for the modelling and simulation of such events, as they propagate through a field of background noise. In practice, the initiator of the SE event may take many forms, such as an earthquake, tsunami, erroneous release of pollution into the environment, etc.. The thesis, thereafter, considers the PR of these events from two perspectives; namely those of binary and one-class classification. The thesis contains an empirical demonstration of all these concepts, based on the exemplary scenario that is suggested by the verification of the Comprehensive Test-Ban-Treaty (CTBT).