We present an improved version of the nested sampling algorithm
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Abstract nessai in which the core algorithm is modified to use importance weights. In the modified algorithm, samples are drawn from a mixture of normalising flows and the requirement for samples to be independently and identically distributed (i.i.d.) according to the prior is relaxed. Furthermore, it allows for samples to be added in any order, independently of a likelihood constraint, and for the evidence to be updated with batches of samples. We call the modified algorithmi-nessai . We first validatei-nessai using analytic likelihoods with known Bayesian evidences and show that the evidence estimates are unbiased in up to 32 dimensions. We comparei-nessai to standardnessai for the analytic likelihoods and the Rosenbrock likelihood, the results show thati-nessai is consistent withnessai whilst producing more precise evidence estimates. We then testi-nessai on 64 simulated gravitational-wave signals from binary black hole coalescence and show that it produces unbiased estimates of the parameters. We compare our results to those obtained using standardnessai anddynesty and find thati-nessai requires 2.68 and 13.3 times fewer likelihood evaluations to converge, respectively. We also testi-nessai of an 80 s simulated binary neutron star signal using a reduced-order-quadrature basis and find that, on average, it converges in 24 min, whilst only requiring likelihood evaluations compared to fornessai and fordynesty . These results demonstrate thati-nessai is consistent withnessai anddynesty whilst also being more efficient.