  Electromagnetic observations have provided strong evidence for the existence
of massive black holes in the center of galaxies, but their origin is still
poorly known. Different scenarios for the formation and evolution of massive
black holes lead to different predictions for their properties and merger
rates. LISA observations of coalescing massive black hole binaries could be
used to reverse engineer the problem and shed light on these mechanisms. In
this paper, we introduce a pipeline based on hierarchical Bayesian inference to
infer the mixing fraction between different theoretical models by comparing
them to LISA observations of massive black hole mergers. By testing this
pipeline against simulated LISA data, we show that it allows us to accurately
infer the properties of the massive black hole population as long as our
theoretical models provide a reliable description of the Universe. We also show
that measurement errors, including both instrumental noise and weak lensing
errors, have little impact on the inference.
