  We present a novel method for sampling iso-likelihood contours in nested
sampling using a type of machine learning algorithm known as normalising flows
and incorporate it into our sampler nessai. Nessai is designed for problems
where computing the likelihood is computationally expensive and therefore the
cost of training a normalising flow is offset by the overall reduction in the
number of likelihood evaluations. We validate our sampler on 128 simulated
gravitational wave signals from compact binary coalescence and show that it
produces unbiased estimates of the system parameters. Subsequently, we compare
our results to those obtained with dynesty and find good agreement between the
computed log-evidences whilst requiring 2.07 times fewer likelihood
evaluations. We also highlight how the likelihood evaluation can be
parallelised in nessai without any modifications to the algorithm. Finally, we
outline diagnostics included in nessai and how these can be used to tune the
sampler's settings.
