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STS426 Guillaume B.

A statistically robust approach to the detection
of astrophysical transient and periodic
phenomena
Guillaume Belanger
European Space Agency (ESAC), Madrid, Spain – gbelanger@sciops.esa.int

Abstract
Transient phenomena are interesting and potentially highly revealing of
details about the processes under study that could otherwise go unnoticed. It
is therefore important to maximise the sensitivity of the detection methods
used. We present a general procedure based on the likelihood function for
identifying transients that is ideally suited for real-time applications because
it requires no grouping or pre-processing of the data. The method use all the
information 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 short-lived
quasi-periodic oscillation in a power spectrum. We present two new
2
periodogram statistics, the ℛ and the Ƶ , and derive two fit statistics, the K
2

and B statistics, relevant to model fitting in frequency space.

Keywords
Transient phenomena; periodic phenomena; likelihood function; astrophysics;
X-rays.

1. Introduction
The way in which the measurements are distributed defines the
appropriate statistical treatment. Each measurement considered individually,
and the collection of measurements as a whole, carry statistical evidence that
can be used to assess the agreement between a given hypothesis or model
and the data. Treating data as evidence is a powerful means to detect changes,
differences, deviations or variations. This is done using the likelihood function.
The detection of an event localized in time, involves identifying something
that was not there before. Whether it rises, dwells, and decays over weeks and
months like a supernova, or whether it just appears and disappears in a
fraction of a second like a -ray burst; whether it manifests as a complete
change of shape of the energy spectrum during a state transition in a black
hole, or as the short-lived emission line from an accretion event; whether it
comes as a sudden change of spectral index in the power spectrum or as the
appearance of an ephemeral quasi-periodic oscillation (QPO); all of these

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