We present an investigation of sample selection effects that influence the
observed black hole - bulge relations and its evolution with redshift. We
provide a common framework in which all kinds of selection effects on the
BH-bulge relations can be investigated, but our main emphasis is on the
consequences of using broad-line AGN and their host galaxies to search for
evolution in the BH-bulge relation. We identified relevant sources of bias that
were not discussed in the literature so far. A particularly important effect is
caused by the fact that the active fraction among SMBHs varies considerably
with BH mass, in the sense that high-mass BHs are less likely to be active than
lower mass ones. In the connection with intrinsic scatter of the BH-bulge
relation this effect implies a bias towards a low BH mass at given bulge
property. This effect adds to the bias caused by working with luminosity or
flux limited samples that were already discussed by others. A quantitative
prediction of these biases requires (i) a realistic model of the sample
selection function, and (ii) knowledge of relevant underlying distribution
functions. For low-redshift AGN samples we can naturally reproduce the
flattening of the relation observed in some studies. When extending our
analysis to higher redshift samples we are clearly hampered by limited
empirical constraints on the various relevant distribution functions. Using a
best-guess approach for these distributions we estimate the expected magnitude
of sample selection biases for a number of recent observational attempts to
study the BH-bulge evolution. In no case do we find statistically significant
evidence for an evolving BH-bulge relation. We suggest a possible practical
approach to circumvent several of the most problematic issues connected with
AGN selection; this could become a powerful diagnostic in future investigations
(abridged).Comment: 20 pages, 20 figures, accepted for publication in A&
