  The space-based gravitational wave detector LISA will observe mergers of
massive black hole binary systems (MBHBs) to cosmological distances, as well as
inspiralling stellar-origin (or stellar-mass) binaries (SBHBs) years before
they enter the LIGO/Virgo band. Much remains to be explored for the parameter
recovery of both classes of systems. Previous MBHB analyses relied on
inspiral-only signals and/or a simplified Fisher matrix analysis, while SBHBs
have not yet been extensively analyzed with Bayesian methods. We accelerate
likelihood computations by (i) using a Fourier-domain response of the LISA
instrument, (ii) using a reduced-order model for non-spinning waveforms that
include a merger-ringdown and higher harmonics, (iii) setting the noise
realization to zero and computing overlaps in the amplitude/phase
representation. We present the first simulations of Bayesian inference for the
parameters of massive black hole systems including consistently the merger and
ringdown of the signal, as well as higher harmonics. We clarify the roles of
LISA response time and frequency dependencies in breaking degeneracies and
illustrate how degeneracy breaking unfolds over time. We also find that
restricting the merger-dominated signal to its dominant harmonic can make the
extrinsic likelihood very degenerate. Including higher harmonics proves to be
crucial to break degeneracies and considerably improves the localization of the
source, with a surviving bimodality in the sky position. We also present
simulations of Bayesian inference for the extrinsic parameters of SBHBs, and
show that although unimodal, their posterior distributions can have
non-Gaussian features.
