{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T00:38:24Z","timestamp":1783730304126,"version":"3.55.0"},"reference-count":80,"publisher":"IOP Publishing","issue":"3","license":[{"start":{"date-parts":[[2023,7,25]],"date-time":"2023-07-25T00:00:00Z","timestamp":1690243200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,7,25]],"date-time":"2023-07-25T00:00:00Z","timestamp":1690243200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"National Science Foundation","award":["PHY-0757058"],"award-info":[{"award-number":["PHY-0757058"]}]},{"DOI":"10.13039\/501100000921","name":"European Cooperation in Science and Technology","doi-asserted-by":"crossref","award":["CA17137"],"award-info":[{"award-number":["CA17137"]}],"id":[{"id":"10.13039\/501100000921","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Science and Technology Research Council","award":["ST\/V005634\/1"],"award-info":[{"award-number":["ST\/V005634\/1"]}]},{"DOI":"10.13039\/501100000271","name":"Science and Technology Facilities Council","doi-asserted-by":"crossref","award":["2285031"],"award-info":[{"award-number":["2285031"]}],"id":[{"id":"10.13039\/501100000271","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2023,9,1]]},"abstract":"Abstract<\/jats:title>\n We present an improved version of the nested sampling algorithm nessai<\/jats:monospace> 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 algorithm i-nessai<\/jats:monospace>. We first validate i-nessai<\/jats:monospace> using analytic likelihoods with known Bayesian evidences and show that the evidence estimates are unbiased in up to 32 dimensions. We compare i-nessai<\/jats:monospace> to standard nessai<\/jats:monospace> for the analytic likelihoods and the Rosenbrock likelihood, the results show that i-nessai<\/jats:monospace> is consistent with nessai<\/jats:monospace> whilst producing more precise evidence estimates. We then test i-nessai<\/jats:monospace> 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 standard nessai<\/jats:monospace> and dynesty<\/jats:monospace> and find that i-nessai<\/jats:monospace> requires 2.68 and 13.3 times fewer likelihood evaluations to converge, respectively. We also test i-nessai<\/jats:monospace> of an 80\u2009s simulated binary neutron star signal using a reduced-order-quadrature basis and find that, on average, it converges in 24\u2009min, whilst only requiring \n \n \n 1.01<\/mml:mn>\n \u00d7<\/mml:mo>\n \n 10<\/mml:mn>\n \n 6<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math>\n \n <\/jats:inline-formula> likelihood evaluations compared to \n \n \n 1.42<\/mml:mn>\n \u00d7<\/mml:mo>\n \n 10<\/mml:mn>\n \n 6<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math>\n \n <\/jats:inline-formula> for nessai<\/jats:monospace> and \n \n \n 4.30<\/mml:mn>\n \u00d7<\/mml:mo>\n \n 10<\/mml:mn>\n \n 7<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math>\n \n <\/jats:inline-formula> for dynesty<\/jats:monospace>. These results demonstrate that i-nessai<\/jats:monospace> is consistent with nessai<\/jats:monospace> and dynesty<\/jats:monospace> whilst also being more efficient.<\/jats:p>","DOI":"10.1088\/2632-2153\/acd5aa","type":"journal-article","created":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T22:44:41Z","timestamp":1684190681000},"page":"035011","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":42,"title":["Importance nested sampling with normalising flows"],"prefix":"10.1088","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2198-2974","authenticated-orcid":true,"given":"Michael J","family":"Williams","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6508-0713","authenticated-orcid":false,"given":"John","family":"Veitch","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7488-5022","authenticated-orcid":true,"given":"Chris","family":"Messenger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2023,7,25]]},"reference":[{"key":"mlstacd5aabib1","first-page":"pp 395","article-title":"Nested Sampling","volume":"vol 735","author":"Skilling","year":"2004","edition":"ed"},{"key":"mlstacd5aabib2","doi-asserted-by":"publisher","first-page":"833","DOI":"10.1214\/06-BA127","article-title":"Nested sampling for general Bayesian computation","volume":"1","author":"Skilling","year":"2006","journal-title":"Bayesian Anal."},{"key":"mlstacd5aabib3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.91.042003","article-title":"Parameter estimation for compact binaries with ground-based gravitational-wave observations using the LALInference software library","volume":"91","author":"Veitch","year":"2015","journal-title":"Phys. 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