{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T15:08:47Z","timestamp":1791558527286,"version":"4.3.4"},"reference-count":71,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000781","name":"ERC","doi-asserted-by":"publisher","award":["101076564"],"award-info":[{"award-number":["101076564"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"ERC","doi-asserted-by":"publisher","award":["101041064"],"award-info":[{"award-number":["101041064"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"name":"MUR-PRIN 2022","award":["2022KBTEBN"],"award-info":[{"award-number":["2022KBTEBN"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Popular deterministic approximations of posterior distributions from, e.g. the Laplace method, variational Bayes and expectation-propagation, generally rely on symmetric families, often taken to be Gaussian. This choice facilitates optimization and inference, but typically affects the quality of the approximation. In fact, even in basic parametric models, posterior distributions often display asymmetries that yield bias and reduced accuracy when considering symmetric approximations. Recent research has moved towards more flexible approximations incorporating skewness. However, current solutions are often model specific, lack general supporting theory, increase the computational complexity of the optimization problem, and do not provide broadly applicable solutions to incorporate skewness in any symmetric approximation. This article addresses such a gap by introducing a general and provably optimal strategy to perturb any symmetric approximation of a generic posterior distribution. The proposed solution is derived without additional optimization steps, and yields a similarly tractable approximation within the class of skew-symmetric densities that enhances the finite sample accuracy of the original symmetric counterpart. Furthermore, under suitable assumptions, it improves the convergence rate to the exact posterior by at least a n factor, in asymptotic regimes. These advancements are illustrated in numerical studies focusing on skewed perturbations of state-of-the-art Gaussian approximations.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkaf082","type":"journal-article","created":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T12:55:30Z","timestamp":1766148930000},"page":"1181-1209","source":"Crossref","is-referenced-by-count":3,"title":["Skew-symmetric approximations of posterior distributions"],"prefix":"10.1093","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8109-6849","authenticated-orcid":false,"given":"Francesco","family":"Pozza","sequence":"first","affiliation":[{"name":"Bocconi Institute for Data Science and Analytics, Bocconi University , Via Roentgen 1, 20136 Milan ,","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8595-6719","authenticated-orcid":false,"given":"Daniele","family":"Durante","sequence":"additional","affiliation":[{"name":"Bocconi Institute for Data Science and Analytics, Bocconi University , Via Roentgen 1, 20136 Milan ,","place":["Italy"]},{"name":"Department of Decision Sciences, Bocconi University , Via Roentgen 1, 20136 Milan ,","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5526-8747","authenticated-orcid":false,"given":"Botond","family":"Szabo","sequence":"additional","affiliation":[{"name":"Bocconi Institute for Data Science and Analytics, Bocconi University , Via Roentgen 1, 20136 Milan ,","place":["Italy"]},{"name":"Department of Decision Sciences, Bocconi University , Via Roentgen 1, 20136 Milan ,","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,1,14]]},"reference":[{"issue":"542","key":"2026091606120663900_qkaf082-B1","doi-asserted-by":"publisher","first-page":"1451","DOI":"10.1080\/01621459.2023.2169150","article-title":"Bayesian conjugacy in probit, tobit, multinomial probit and extensions: A review and new results","volume":"118","author":"Anceschi","year":"2023","journal-title":"Journal of the American Statistical Association"},{"issue":"3","key":"2026091606120663900_qkaf082-B2","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1111\/j.1467-9469.2006.00503.x","article-title":"On the unification of families of skew-normal distributions","volume":"33","author":"Arellano-Valle","year":"2006","journal-title":"Scandinavian Journal of Statistics"},{"issue":"3","key":"2026091606120663900_qkaf082-B3","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1111\/1467-9868.00194","article-title":"Statistical applications of the multivariate skew normal distribution","volume":"61","author":"Azzalini","year":"1999","journal-title":"Journal of the Royal Statistical Society: Series B, Statistical Methodology"},{"issue":"2","key":"2026091606120663900_qkaf082-B4","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1111\/1467-9868.00391","article-title":"Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution","volume":"65","author":"Azzalini","year":"2003","journal-title":"Journal of the Royal Statistical Society: Series B, Statistical Methodology"},{"key":"2026091606120663900_qkaf082-B5","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139248891","volume-title":"The skew-normal and related families","author":"Azzalini","year":"2013"},{"issue":"4","key":"2026091606120663900_qkaf082-B6","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1093\/biomet\/83.4.715","article-title":"The multivariate skew-normal distribution","volume":"83","author":"Azzalini","year":"1996","journal-title":"Biometrika"},{"key":"2026091606120663900_qkaf082-B7","volume-title":"Pattern recognition and machine learning","author":"Bishop","year":"2006"},{"issue":"518","key":"2026091606120663900_qkaf082-B8","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1080\/01621459.2017.1285773","article-title":"Variational inference: A review for statisticians","volume":"112","author":"Blei","year":"2017","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"2026091606120663900_qkaf082-B9","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1214\/12-BA703","article-title":"Scalable variational inference for Bayesian variable selection in regression, and its accuracy in genetic association studies","volume":"7","author":"Carbonetto","year":"2012","journal-title":"Bayesian Analysis"},{"key":"2026091606120663900_qkaf082-B10","first-page":"1","article-title":"Affine independent variational inference","volume":"25","author":"Challis","year":"2012","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"68","key":"2026091606120663900_qkaf082-B11","first-page":"2239","article-title":"Gaussian Kullback\u2013Leibler approximate inference","volume":"14","author":"Challis","year":"2013","journal-title":"Journal of Machine Learning Research"},{"key":"2026091606120663900_qkaf082-B12","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-030-47845-2","volume-title":"An introduction to sequential Monte Carlo","author":"Chopin","year":"2020"},{"issue":"1","key":"2026091606120663900_qkaf082-B13","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1214\/16-STS581","article-title":"Leave Pima Indians alone: Binary regression as a benchmark for Bayesian computation","volume":"32","author":"Chopin","year":"2017","journal-title":"Statistical Science"},{"issue":"6","key":"2026091606120663900_qkaf082-B14","doi-asserted-by":"publisher","first-page":"1532","DOI":"10.3390\/e12061532","article-title":"Families of alpha-beta-and gamma-divergences: Flexible and robust measures of similarities","volume":"12","author":"Cichocki","year":"2010","journal-title":"Entropy"},{"issue":"2","key":"2026091606120663900_qkaf082-B15","doi-asserted-by":"publisher","first-page":"790","DOI":"10.1016\/j.csda.2006.10.028","article-title":"Mean-field variational approximate Bayesian inference for latent variable models","volume":"52","author":"Consonni","year":"2007","journal-title":"Computational Statistics & Data Analysis"},{"issue":"64","key":"2026091606120663900_qkaf082-B16","first-page":"1","article-title":"Monotonic alpha-divergence minimisation for variational inference","volume":"24","author":"Daudel","year":"2023","journal-title":"Journal of Machine Learning Research"},{"issue":"1","key":"2026091606120663900_qkaf082-B17","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1111\/rssb.12241","article-title":"Expectation propagation in the large data limit","volume":"80","author":"Dehaene","year":"2018","journal-title":"Journal of the Royal Statistical Society: Series B, Statistical Methodology"},{"key":"2026091606120663900_qkaf082-B18","first-page":"1","article-title":"t-divergence based approximate inference","volume":"24","author":"Ding","year":"2011","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"6","key":"2026091606120663900_qkaf082-B19","doi-asserted-by":"publisher","first-page":"2714","DOI":"10.1214\/24-AOS2429","article-title":"Skewed Bernstein-von Mises theorem and skew-modal approximations","volume":"52","author":"Durante","year":"2024","journal-title":"Annals of Statistics"},{"issue":"3","key":"2026091606120663900_qkaf082-B20","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1214\/19-STS712","article-title":"Conditionally conjugate mean-field variational Bayes for logistic models","volume":"34","author":"Durante","year":"2019","journal-title":"Statistical Science"},{"issue":"30","key":"2026091606120663900_qkaf082-B21","first-page":"1","article-title":"A class of conjugate priors for multinomial probit models which includes the multivariate normal one","volume":"23","author":"Fasano","year":"2022","journal-title":"Journal of Machine Learning Research"},{"issue":"4","key":"2026091606120663900_qkaf082-B22","doi-asserted-by":"publisher","first-page":"901","DOI":"10.1093\/biomet\/asac026","article-title":"Scalable and accurate variational Bayes for high-dimensional binary regression models","volume":"109","author":"Fasano","year":"2022","journal-title":"Biometrika"},{"key":"2026091606120663900_qkaf082-B23","first-page":"1","article-title":"Expectation propagation for t-exponential family using q-algebra","volume":"30","author":"Futami","year":"2017","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"2","key":"2026091606120663900_qkaf082-B24","doi-asserted-by":"publisher","first-page":"363","DOI":"10.2307\/1913241","article-title":"Semi-nonparametric maximum likelihood estimation","volume":"55","author":"Gallant","year":"1987","journal-title":"Econometrica: Journal of the Econometric Society"},{"key":"2026091606120663900_qkaf082-B25","doi-asserted-by":"crossref","DOI":"10.1201\/b16018","volume-title":"Bayesian data analysis","author":"Gelman","year":"2013","edition":"3rd ed."},{"issue":"2","key":"2026091606120663900_qkaf082-B26","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/BF02507031","article-title":"Generalized skew-elliptical distributions and their quadratic forms","volume":"57","author":"Genton","year":"2005","journal-title":"Annals of the Institute of Statistical Mathematics"},{"issue":"51","key":"2026091606120663900_qkaf082-B27","first-page":"1","article-title":"Covariances, robustness and variational Bayes","volume":"19","author":"Giordano","year":"2018","journal-title":"Journal of Machine Learning Research"},{"issue":"2","key":"2026091606120663900_qkaf082-B28","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1016\/j.jspi.2003.09.008","article-title":"Additive properties of skew normal random vectors","volume":"126","author":"Gonz\u00e1lez-Farias","year":"2004","journal-title":"Journal of Statistical Planning and Inference"},{"key":"2026091606120663900_qkaf082-B29","author":"Hernandez-Lobato","year":"2016"},{"issue":"3","key":"2026091606120663900_qkaf082-B30","doi-asserted-by":"publisher","first-page":"680","DOI":"10.1093\/biomet\/63.3.680","article-title":"On estimating a symmetric distribution","volume":"63","author":"Hinkley","year":"1976","journal-title":"Biometrika"},{"issue":"87","key":"2026091606120663900_qkaf082-B31","first-page":"1","article-title":"How good is your Gaussian approximation of the posterior? Finite-sample computable error bounds for a variety of useful divergences","volume":"26","author":"Kasprzak","year":"2025","journal-title":"Journal of Machine Learning Research"},{"key":"2026091606120663900_qkaf082-B32","doi-asserted-by":"publisher","author":"Katsevich","year":"2024","DOI":"10.48550\/arXiv.2306.07262"},{"issue":"4","key":"2026091606120663900_qkaf082-B33","doi-asserted-by":"publisher","first-page":"1384","DOI":"10.1214\/24-AOS2393","article-title":"On the approximation accuracy of Gaussian variational inference","volume":"52","author":"Katsevich","year":"2024","journal-title":"Annals of Statistics"},{"key":"2026091606120663900_qkaf082-B34","doi-asserted-by":"publisher","author":"Kock","year":"2025","DOI":"10.48550\/arXiv.2503.18075"},{"issue":"14","key":"2026091606120663900_qkaf082-B35","first-page":"1","article-title":"Automatic differentiation variational inference","volume":"18","author":"Kucukelbir","year":"2017","journal-title":"Journal of Machine Learning Research"},{"issue":"1","key":"2026091606120663900_qkaf082-B36","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On information and sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"The Annals of Mathematical Statistics"},{"issue":"1","key":"2026091606120663900_qkaf082-B37","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/s11135-010-9324-x","article-title":"Zero-inflated count regression models with applications to some examples","volume":"46","author":"Lawal","year":"2012","journal-title":"Quality & Quantity"},{"key":"2026091606120663900_qkaf082-B38","author":"Liang","year":"2022"},{"issue":"3","key":"2026091606120663900_qkaf082-B39","doi-asserted-by":"publisher","first-page":"1097","DOI":"10.1214\/aos\/1176349658","article-title":"Estimation of a symmetric distribution","volume":"13","author":"Lo","year":"1985","journal-title":"Annals of Statistics"},{"issue":"3","key":"2026091606120663900_qkaf082-B40","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1111\/sjos.2004.31.issue-3","article-title":"Flexible class of skew-symmetric distributions","volume":"31","author":"Ma","year":"2004","journal-title":"Scandinavian Journal of Statistics"},{"issue":"202","key":"2026091606120663900_qkaf082-B41","first-page":"1","article-title":"Variational inference for uncertainty quantification: An analysis of trade-offs","volume":"26","author":"Margossian","year":"2025","journal-title":"Journal of Machine Learning Research"},{"key":"2026091606120663900_qkaf082-B42","author":"Minka","year":"2001"},{"issue":"3","key":"2026091606120663900_qkaf082-B43","doi-asserted-by":"publisher","first-page":"786","DOI":"10.1162\/neco.2008.08-07-592","article-title":"The variational Gaussian approximation revisited","volume":"21","author":"Opper","year":"2009","journal-title":"Neural Computation"},{"key":"2026091606120663900_qkaf082-B44","author":"Ormerod","year":"2011"},{"issue":"3","key":"2026091606120663900_qkaf082-B45","doi-asserted-by":"publisher","first-page":"665","DOI":"10.1214\/14-BA926","article-title":"Finite sample Bernstein\u2013von Mises theorem for semiparametric problems","volume":"10","author":"Panov","year":"2015","journal-title":"Bayesian Analysis"},{"issue":"57","key":"2026091606120663900_qkaf082-B46","first-page":"1","article-title":"Normalizing flows for probabilistic modeling and inference","volume":"22","author":"Papamakarios","year":"2021","journal-title":"Journal of Machine Learning Research"},{"key":"2026091606120663900_qkaf082-B47","author":"P\u00f3czos","year":"2011"},{"key":"2026091606120663900_qkaf082-B48","author":"Ranganath","year":"2014"},{"issue":"539","key":"2026091606120663900_qkaf082-B49","doi-asserted-by":"publisher","first-page":"1270","DOI":"10.1080\/01621459.2020.1847121","article-title":"Variational Bayes for high-dimensional linear regression with sparse priors","volume":"117","author":"Ray","year":"2022","journal-title":"Journal of the American Statistical Association"},{"key":"2026091606120663900_qkaf082-B50","author":"Rezende","year":"2015"},{"issue":"1","key":"2026091606120663900_qkaf082-B51","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1111\/rssa.12361","article-title":"Bayesian semiparametric modelling of contraceptive behaviour in India via sequential logistic regressions","volume":"182","author":"Rigon","year":"2019","journal-title":"Journal of the Royal Statistical Society: Series A, Statistics in Society"},{"issue":"4","key":"2026091606120663900_qkaf082-B52","doi-asserted-by":"publisher","first-page":"853","DOI":"10.1111\/rssb.12466","article-title":"Approximate Laplace approximations for scalable model selection","volume":"83","author":"Rossell","year":"2021","journal-title":"Journal of the Royal Statistical Society: Series B, Statistical Methodology"},{"issue":"2","key":"2026091606120663900_qkaf082-B53","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1111\/j.1467-9868.2008.00700.x","article-title":"Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations","volume":"71","author":"Rue","year":"2009","journal-title":"Journal of the Royal Statistical Society: Series B, Statistical Methodology"},{"issue":"2","key":"2026091606120663900_qkaf082-B54","doi-asserted-by":"publisher","first-page":"3986","DOI":"10.1214\/16-EJS1218","article-title":"Improved Laplace approximation for marginal likelihoods","volume":"10","author":"Ruli","year":"2016","journal-title":"Electronic Journal of Statistics"},{"issue":"4","key":"2026091606120663900_qkaf082-B55","doi-asserted-by":"publisher","first-page":"1329","DOI":"10.1080\/10618600.2024.2319159","article-title":"Structured variational approximations with skew normal decomposable graphical models","volume":"33","author":"Salomone","year":"2024","journal-title":"Journal of Computational and Graphical Statistics"},{"issue":"3","key":"2026091606120663900_qkaf082-B56","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1093\/biomet\/62.3.631","article-title":"Estimating the distribution function of a symmetric distribution","volume":"62","author":"Schuster","year":"1975","journal-title":"Biometrika"},{"issue":"2","key":"2026091606120663900_qkaf082-B57","doi-asserted-by":"publisher","first-page":"865","DOI":"10.1214\/aos\/1176350380","article-title":"Identifying the closest symmetric distribution or density function","volume":"15","author":"Schuster","year":"1987","journal-title":"Annals of Statistics"},{"issue":"4","key":"2026091606120663900_qkaf082-B58","doi-asserted-by":"publisher","first-page":"729","DOI":"10.1080\/10618600.2020.1740097","article-title":"High-dimensional copula variational approximation through transformation","volume":"29","author":"Smith","year":"2020","journal-title":"Journal of Computational and Graphical Statistics"},{"issue":"1","key":"2026091606120663900_qkaf082-B59","doi-asserted-by":"publisher","first-page":"1303","DOI":"10.1214\/23-BA1391","article-title":"Inexact Laplace approximation and the use of posterior mean in Bayesian inference","volume":"20","author":"Spokoiny","year":"2025","journal-title":"Bayesian Analysis"},{"issue":"2","key":"2026091606120663900_qkaf082-B60","doi-asserted-by":"publisher","first-page":"843","DOI":"10.3150\/21-BEJ1412","article-title":"Accuracy of Gaussian approximation for high-dimensional posterior distributions","volume":"31","author":"Spokoiny","year":"2025","journal-title":"Bernoulli"},{"issue":"2","key":"2026091606120663900_qkaf082-B61","doi-asserted-by":"publisher","first-page":"422","DOI":"10.1080\/10618600.2024.2402278","article-title":"Variational inference based on a subclass of closed skew normals","volume":"34","author":"Tan","year":"2024","journal-title":"Journal of Computational and Graphical Statistics"},{"issue":"2","key":"2026091606120663900_qkaf082-B62","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/s11222-017-9729-7","article-title":"Gaussian variational approximation with sparse precision matrices","volume":"28","author":"Tan","year":"2018","journal-title":"Statistics and Computing"},{"issue":"393","key":"2026091606120663900_qkaf082-B63","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1080\/01621459.1986.10478240","article-title":"Accurate approximations for posterior moments and marginal densities","volume":"81","author":"Tierney","year":"1986","journal-title":"Journal of the American Statistical Association"},{"key":"2026091606120663900_qkaf082-B64","volume-title":"Asymptotic statistics","author":"Van der Vaart","year":"2000"},{"issue":"17","key":"2026091606120663900_qkaf082-B65","first-page":"1","article-title":"Expectation propagation as a way of life: A framework for Bayesian inference on partitioned data","volume":"21","author":"Vehtari","year":"2020","journal-title":"Journal of Machine Learning Research"},{"issue":"1","key":"2026091606120663900_qkaf082-B66","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1111\/j.2517-6161.1969.tb00767.x","article-title":"On the asymptotic behaviour of posterior distributions","volume":"31","author":"Walker","year":"1969","journal-title":"Journal of the Royal Statistical Society: Series B, Statistical Methodology"},{"issue":"32","key":"2026091606120663900_qkaf082-B67","first-page":"1005","article-title":"Variational inference in nonconjugate models","volume":"14","author":"Wang","year":"2013","journal-title":"Journal of Machine Learning Research"},{"issue":"4","key":"2026091606120663900_qkaf082-B68","first-page":"1259","article-title":"A skew-symmetric representation of multivariate distributions","volume":"14","author":"Wang","year":"2004","journal-title":"Statistica Sinica"},{"issue":"527","key":"2026091606120663900_qkaf082-B69","doi-asserted-by":"publisher","first-page":"1147","DOI":"10.1080\/01621459.2018.1473776","article-title":"Frequentist consistency of variational Bayes","volume":"114","author":"Wang","year":"2019","journal-title":"Journal of the American Statistical Association"},{"issue":"2","key":"2026091606120663900_qkaf082-B70","doi-asserted-by":"publisher","first-page":"886","DOI":"10.1214\/19-AOS1827","article-title":"\u03b1-variational inference with statistical guarantees","volume":"48","author":"Yang","year":"2020","journal-title":"Annals of Statistics"},{"issue":"5","key":"2026091606120663900_qkaf082-B71","doi-asserted-by":"publisher","first-page":"1016","DOI":"10.1080\/00949655.2023.2277885","article-title":"Tractable skew-normal approximations via matching","volume":"94","author":"Zhou","year":"2024","journal-title":"Journal of Statistical Computation and Simulation"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/88\/4\/1181\/66413861\/qkaf082.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/88\/4\/1181\/66413861\/qkaf082.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T10:12:15Z","timestamp":1789553535000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/88\/4\/1181\/8425622"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,14]]},"references-count":71,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2026,1,14]]},"published-print":{"date-parts":[[2026,9,16]]}},"URL":"https:\/\/doi.org\/10.1093\/jrsssb\/qkaf082","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,9]]},"published":{"date-parts":[[2026,1,14]]}}}