  We seek to achieve the Holy Grail of Bayesian inference for
gravitational-wave astronomy: using deep-learning techniques to instantly
produce the posterior $p(\theta|D)$ for the source parameters $\theta$, given
the detector data $D$. To do so, we train a deep neural network to take as
input a signal + noise data set (drawn from the astrophysical source-parameter
prior and the sampling distribution of detector noise), and to output a
parametrized approximation of the corresponding posterior. We rely on a compact
representation of the data based on reduced-order modeling, which we generate
efficiently using a separate neural-network waveform interpolant [A. J. K.
Chua, C. R. Galley & M. Vallisneri, Phys. Rev. Lett. 122, 211101 (2019)]. Our
scheme has broad relevance to gravitational-wave applications such as
low-latency parameter estimation and characterizing the science returns of
future experiments. Source code and trained networks are available online at
https://github.com/vallis/truebayes.
