  The population properties of intermediate mass black holes remain largely
unknown, and understanding their distribution could provide a missing link in
the formation of supermassive black holes and galaxies. Gravitational wave
observations can help fill in the gap from stellar mass black holes to
supermassive black holes. In our work, we propose a new method for probing lens
populations through lensing statistics of gravitational waves, here focusing on
inferring the number density of intermediate mass black holes. Using
hierarchical Bayesian inference of injected lensed gravitational waves, we find
that existing gravitational wave observatories at design sensitivity could
either identify an injected number density of $10^6 \mathrm{Mpc}^{-3}$ or place
an upper bound of $\lesssim 10^4 \mathrm{Mpc}^{-3}$ for an injected $10^3
\mathrm{Mpc}^{-3}$. More broadly, our method could be applied to probe other
forms of compact matter as well.
