  Pulsar timing arrays (PTAs) perform Bayesian posterior inference with
expensive MCMC methods. Given a dataset of ~10-100 pulsars and O(10^3) timing
residuals each, producing a posterior distribution for the stochastic
gravitational wave background (SGWB) can take days to a week. The computational
bottleneck arises because the likelihood evaluation required for MCMC is
extremely costly when considering the dimensionality of the search space.
Fortunately, generating simulated data is fast, so modern simulation-based
inference techniques can be brought to bear on the problem. In this paper, we
demonstrate how conditional normalizing flows trained on simulated data can be
used for extremely fast and accurate estimation of the SGWB posteriors,
reducing the sampling time from weeks to a matter of seconds.
