On Detecting Transient Phenomena

Transient phenomena are interesting and potentially highly revealing of details about the processes under observation and study that could otherwise go unnoticed. It is therefore important to maximize the sensitivity of the method used to identify such events. In this article, we present a general procedure based on the use of the likelihood function for identifying transients which is particularly suited for real-time applications because it requires no grouping or pre-processing of the data. The method makes use of all the information that is available in the data throughout the statistical decision-making process, and is suitable for a wide range of applications. Here we consider those most common in astrophysics, which involve searching for transient sources, events or features in images, time series, energy spectra, and power spectra, and demonstrate the use of the method in the case of a weak X-ray flare in a time series and a short-lived quasi-periodic oscillation in a power spectrum. We derive a fit statistic that is ideal for fitting arbitrarily shaped models to a power density distribution, which is of general interest in all applications involving periodogram analysis.