Bayesian analysis of LIGO-Virgo mergers: Primordial vs. astrophysical
  black hole populations
  We conduct a thorough Bayesian analysis of the possibility that the black
hole merger events seen in gravitational waves are primordial black hole (PBH)
mergers. Using the latest merger rate models for PBH binaries drawn from a
lognormal mass function we compute posterior parameter constraints and Bayesian
evidences using data from the first two observing runs of LIGO-Virgo. We
account for theoretical uncertainty due to possible disruption of the binary by
surrounding PBHs, which can suppress the merger rate significantly. We also
consider simple astrophysically motivated models and find that these are
favoured decisively over the PBH scenario, quantified by the Bayesian evidence
ratio. Paying careful attention to the influence of the parameter priors and
the quality of the model fits, we show that the evidence ratios can be
understood by comparing the predicted chirp mass distribution to that of the
data. We identify the posterior predictive distribution of chirp mass as a
vital tool for discriminating between models. A model in which all mergers are
PBH binaries is strongly disfavoured compared with astrophysical models, in
part due to the over-prediction of heavy systems having $\mathcal{M}_{{\rm
chirp}} \gtrsim 40 \, M_\odot$ and positive skewness over the range of observed
masses which does not match the observations. We find that the fit is not
significantly improved by adding a maximum mass cut-off, a bimodal mass
function, or imposing that PBH binaries form at late times. We argue that a
successful PBH model must either modify the lognormal shape of the initial mass
function significantly or abandon the hypothesis that all observed merging
binaries are primordial. We develop and apply techniques for analysing PBH
models with gravitational wave data which will be necessary for robust
statistical inference as the gravitational wave source sample size increases.
