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

Constraining the host galaxy halos of massive black holes from LISA event rates