Characterisation of lensing selection effects for LISA massive black
  hole binary mergers
  We present a method to include lensing selection effects due to the finite
horizon of a given detector when studying lensing of gravitational wave (GW)
sources. When selection effects are included, the mean of the magnification
distribution is shifted from one to higher values for sufficiently
high-redshift sources. This introduces an irreducible (multiplicative) bias on
the luminosity distance reconstruction, in addition to the typical source of
uncertainty in the distance determination. We apply this method to study
lensing of GWs emitted by massive black hole binary mergers at high redshift
detectable by LISA. We estimate the expected bias induced by selection effects
on the luminosity distance reconstruction as function of cosmological redshift,
and discuss its implications for cosmological and astrophysical analyses with
LISA. We also reconstruct the distribution of lensing magnification as a
function of the observed luminosity distance to a source, that is the
observable quantity in the absence of an electromagnetic counterpart. Lensing
provides the dominant source of errors in distance measurements of
high-redshift GW sources. Its full characterisation, including the impact of
selection effects, is of paramount importance to correctly determine the
astrophysical properties of the underlying source population and to be able to
use gravitational wave sources as a new cosmological probe.
