  Variability is a property shared by practically all AGN. This makes
variability selection a possible technique for identifying AGN. Given that
variability selection makes no prior assumption about spectral properties, it
is a powerful technique for detecting both low-luminosity AGN in which the host
galaxy emission is dominating and AGN with unusual spectral properties. In this
paper, we will discuss and test different statistical methods for the detection
of variability in sparsely sampled data that allow full control over the false
positive rates. We will apply these methods to the GOODS North and South fields
and present a catalog of variable sources in the z band in both GOODS fields.
Out of 11931 objects checked, we find 155 variable sources at a significance
level of 99.9%, corresponding to about 1.3% of all objects. After rejection of
stars and supernovae, 139 variability selected AGN remain. Their magnitudes
reach down as faint as 25.5 mag in z. Spectroscopic redshifts are available for
22 of the variability selected AGN, ranging from 0.046 to 3.7. The absolute
magnitudes in the rest-frame z-band range from ~ -18 to -24, reaching
substantially fainter than the typical luminosities probed by traditional X-ray
and spectroscopic AGN selection in these fields. Therefore, this is a powerful
technique for future exploration of the evolution of the faint end of the AGN
luminosity function up to high redshifts.
