  We introduce the Mass-Excitation (MEx) diagnostic to identify active galactic
nuclei (AGN) in galaxies at intermediate redshift. In the absence of
near-infrared spectroscopy, necessary to use traditional nebular line diagrams
at z>0.4, we demonstrate that combining [OIII]5007/Hbeta and stellar mass
successfully distinguishes between star formation and AGN emission. The MEx
classification scheme relies on a novel probabilistic approach splitting
galaxies into sub-categories with more confidence than alternative high-z
diagnostic diagrams. It recognizes that galaxies near empirical boundaries on
traditional diagrams have an uncertain classification and thus a non-zero
probability of belonging to more than one category. An outcome of this work is
a system of statistical weights that can be used to compute global properties
of galaxy samples. We apply the MEx diagram to 2,812 galaxies at 0.3<z<1 in the
Great Observatories Origins Deep Survey North and Extended Groth Strip fields,
and compare it to an independent X-ray classification scheme. We identify
Compton-thick AGN candidates with large X-ray absorption, which we infer from
the luminosity ratio between hard X-ray emission and [OIII]5007, a nearly
isotropic tracer of AGN. X-ray stacking of sources that were not detected
individually supports the validity of the MEx diagram and yields a very flat
spectral slope for the Compton-thick candidates (Gamma~0.4, unambiguously
indicating absorbed AGN). We present evidence that composite galaxies, which
are difficult to identify with alternative high-redshift diagrams, host the
majority of the highly-absorbed AGN. Our findings suggest that the interstellar
medium of the host galaxy provides significant absorption in addition to the
torus invoked in AGN unified models.
