  The coalescence of massive black hole binaries (with masses $10^4 - 10^7
M_{\odot}$) leads to gravitational wave emission that is detectable out to high
redshifts ($z \sim 20$) with the forthcoming LISA observatory. We combine the
theoretically derived merger rates for dark matter haloes at various redshifts,
with an empirically motivated prescription that connects the mass of a dark
matter halo and that of its central black hole. Using the expected constraints
on the (chirp or reduced) masses of binary black holes, their mass ratios and
redshift uncertainties, we forecast the measurement precision on the occupation
fraction, normalization and slope of the black hole mass - halo mass relation
at various redshifts, assuming a five-year LISA survey for three different
confidence scenarios. We use the expected sizes of the LISA localization
ellipses on the sky to estimate the number of electromagnetic counterparts to
the gravitational wave sources which are detectable by future wide-field
optical surveys, such as LSST.
