Is the cluster environment quenching the Seyfert activity in elliptical
  and spiral galaxies?
  We developed a hierarchical Bayesian model (HBM) to investigate how the
presence of Seyfert activity relates to their environment, herein represented
by the galaxy cluster mass, $M_{200}$, and the normalized cluster-centric
distance, $r/r_{200}$. We achieved this by constructing an unbiased sample of
galaxies from the Sloan Digital Sky Survey, with morphological classifications
provided by the Galaxy Zoo Project. A propensity score matching approach is
introduced to control for the effects of confounding variables: stellar mass,
galaxy colour, and star formation rate. The connection between Seyfert-activity
and environmental properties in the de-biased sample is modelled within an HBM
framework using the so-called logistic regression technique, suitable for the
analysis of binary data (e.g., whether or not a galaxy hosts an AGN). Unlike
standard ordinary least square fitting methods, our methodology naturally
allows modelling the probability of Seyfert-AGN activity in galaxies on their
natural scale, i.e. as a binary variable. Furthermore, we demonstrate how an
HBM can incorporate information of each particular galaxy morphological type in
a unified framework. In elliptical galaxies, our analysis indicates a strong
correlation of Seyfert-AGN activity with $r/r_{200}$, and a weaker correlation
with the mass of the host. In spiral galaxies these trends do not appear,
suggesting that the link between Seyfert activity and the properties of spiral
galaxies are independent of the environment.
