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Electromagnetic observations have provided strong evidence for the existenceof massive black holes in the center of galaxies, but their origin is stillpoorly known. Different scenarios for the formation and evolution of massiveblack holes lead to different predictions for their properties and mergerrates. LISA observations of coalescing massive black hole binaries could beused to reverse engineer the problem and shed light on these mechanisms. Inthis paper, we introduce a pipeline based on hierarchical Bayesian inference toinfer the mixing fraction between different theoretical models by comparingthem to LISA observations of massive black hole mergers. By testing thispipeline against simulated LISA data, we show that it allows us to accuratelyinfer the properties of the massive black hole population as long as ourtheoretical models provide a reliable description of the Universe. We also showthat measurement errors, including both instrumental noise and weak lensingerrors, have little impact on the inference.

Discriminating between different scenarios for the formation and evolution of massive black holes with LISA