Constraining the Black Hole Mass Spectrum with LISA Observations II:
  Direct comparison of detailed models
  A number of scenarios have been proposed for the origin of the supermassive
black holes (SMBHs) that are found in the centres of most galaxies. Many such
scenarios predict a high-redshift population of massive black holes (MBHs),
with masses in the range 100 to 100000 times that of the Sun. When the Laser
Interferometer Space Antenna (LISA) is finally operational, it is likely that
it will detect on the order of 100 of these MBH binaries as they merge. The
differences between proposed population models produce appreciable effects in
the portion of the population which is detectable by LISA, so it is likely that
the LISA observations will allow us to place constraints on them. However,
gravitational wave detectors such as LISA will not be able to detect all such
mergers nor assign precise black hole parameters to the merger, due to weak
gravitational wave signal strengths. This paper explores LISA's ability to
distinguish between several MBH population models. In this way, we go beyond
predicting a LISA observed population and consider the extent to which LISA
observations could inform astrophysical modellers. The errors in LISA parameter
estimation are applied with a direct method which generates random sample
parameters for each source in a population realisation. We consider how the
distinguishability varies depending on the choice of source parameters (1 or 2
parameters chosen from masses, redshift or spins) used to characterise the
model distributions, with confidence levels determined by 1 and 2-dimensional
tests based on the Kolmogorov-Smirnov test.
