  Gravitational wave (GW) detection is now commonplace and as the sensitivity
of the global network of GW detectors improves, we will observe
$\mathcal{O}(100)$s of transient GW events per year. The current methods used
to estimate their source parameters employ optimally sensitive but
computationally costly Bayesian inference approaches where typical analyses
have taken between 6 hours and 5 days. For binary neutron star and neutron star
black hole systems prompt counterpart electromagnetic (EM) signatures are
expected on timescales of 1 second -- 1 minute and the current fastest method
for alerting EM follow-up observers, can provide estimates in $\mathcal{O}(1)$
minute, on a limited range of key source parameters. Here we show that a
conditional variational autoencoder pre-trained on binary black hole signals
can return Bayesian posterior probability estimates. The training procedure
need only be performed once for a given prior parameter space and the resulting
trained machine can then generate samples describing the posterior distribution
$\sim 6$ orders of magnitude faster than existing techniques.
