  We propose the usage of an innovative method for selecting transients and
variables. These sources are detected at different wavelengths across the
electromagnetic spectrum spanning from radio waves to gamma-rays. We focus on
radio signals and use State Space Models, which are also referred to as Dynamic
Linear Models. State Space Models (and more generally parametric autoregressive
models) have been the mainstay of economic modelling for some years, but rarely
they have been used in Astrophysics. The statistics currently used to identify
radio variables and transients are not sophisticated enough to distinguish
different types of variability. These methods simply report the overall
modulation and significance of the variability, and the ordering of the data in
time is insignificant. State Space Models are much more advanced and can encode
not only the amount and significance of the variability but also properties,
such as slope, rise or decline for a given time t. In this work, we evaluate
the effectiveness of State Space Models for transient and variable detection
including classification in time-series astronomy. We also propose a method for
detecting a transient source hosted in a variable active galaxy, whereby the
time-series of a static host galaxy and the dynamic nature of the transient in
the galaxy are intertwined. Furthermore, we examine the hypothetical scenario
where the target transient we want to detect is the gravitational wave source
GW170817 (or similar).
