{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T21:39:59Z","timestamp":1766439599704,"version":"3.48.0"},"reference-count":52,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T00:00:00Z","timestamp":1763510400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T00:00:00Z","timestamp":1763510400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004329","name":"The Slovenian Research and Innovation Agency","doi-asserted-by":"publisher","award":["P2-0442"],"award-info":[{"award-number":["P2-0442"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004329","name":"The Slovenian Research and Innovation Agency","doi-asserted-by":"publisher","award":["P2-0442"],"award-info":[{"award-number":["P2-0442"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Mach Learn"],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Recent advances in MCMC use normalizing flows to precondition target distributions and enable jumps to distant regions. However, there is currently no systematic comparison of different normalizing flow architectures for MCMC. As such, many works choose simple flow architectures that are readily available and do not consider other models. Guidelines for choosing an appropriate architecture would reduce analysis time for practitioners and motivate researchers to take the recommended models as foundations to be improved. We provide the first such guideline by extensively evaluating many normalizing flow architectures on various flow-based MCMC methods and target distributions. When the target density gradient is available, we show that flow-based MCMC outperforms classic MCMC for suitable NF architecture choices with minor hyperparameter tuning. When the gradient is unavailable, flow-based MCMC wins with off-the-shelf architectures. We find contractive residual flows to be the best general-purpose models with relatively low sensitivity to hyperparameter choice. We also provide various insights into normalizing flow behavior within MCMC when varying their hyperparameters, properties of target distributions, and the overall computational budget.<\/jats:p>","DOI":"10.1007\/s10994-025-06900-3","type":"journal-article","created":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T22:30:41Z","timestamp":1763591441000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Empirical evaluation of normalizing flows in Markov chain Monte Carlo"],"prefix":"10.1007","volume":"114","author":[{"given":"David","family":"Nabergoj","sequence":"first","affiliation":[]},{"given":"Erik","family":"\u0160trumbelj","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,11,19]]},"reference":[{"issue":"11","key":"6900_CR1","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1140\/epja\/s10050-023-01154-w","volume":"59","author":"R Abbott","year":"2023","unstructured":"Abbott, R., Albergo, M. S., Botev, A., Boyda, D., Cranmer, K., Hackett, D. C., Matthews, A. G. D. G., Racani\u00e8re, S., Razavi, A., Rezende, D. J., Romero-L\u00f3pez, F., Shanahan, P. E., & Urban, J. M. (2023). Aspects of scaling and scalability for flow-based sampling of lattice QCD. The European Physical Journal A, 59(11), 257. https:\/\/doi.org\/10.1140\/epja\/s10050-023-01154-w","journal-title":"The European Physical Journal A"},{"key":"6900_CR2","unstructured":"Agrawal, A., & Domke, J. (2024). Disentangling impact of capacity, objective, batchsize, estimators, and step-size on flow VI. arXiv. arXiv:2412.08824."},{"issue":"3","key":"6900_CR3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.100.034515","volume":"100","author":"MS Albergo","year":"2019","unstructured":"Albergo, M. S., Kanwar, G., & Shanahan, P. E. (2019). Flow-based generative models for Markov chain Monte Carlo in lattice field theory. Physical Review D, 100(3), Article 034515. https:\/\/doi.org\/10.1103\/PhysRevD.100.034515","journal-title":"Physical Review D"},{"issue":"1","key":"6900_CR4","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s11222-014-9521-x","volume":"26","author":"P Alquier","year":"2016","unstructured":"Alquier, P., Friel, N., Everitt, R., & Boland, A. (2016). Noisy Monte Carlo: Convergence of Markov chains with approximate transition kernels. Statistics and Computing, 26(1), 29\u201347. https:\/\/doi.org\/10.1007\/s11222-014-9521-x","journal-title":"Statistics and Computing"},{"key":"6900_CR5","unstructured":"Arbel, M., Matthews, A., & Doucet, A. (2021). Annealed flow transport Monte Carlo. In Proceedings of the 38th International Conference on Machine Learning. Proceedings of Machine Learning Research (vol. 139, pp. 318\u2013330). Vienna, Austria: PMLR (virtual conference)."},{"key":"6900_CR6","unstructured":"Behrmann, J., Grathwohl, W., Chen, R. T. Q., Duvenaud, D., & Jacobsen, J.-H. (2019). Invertible residual networks. In: Proceedings of the 36th International Conference on Machine Learning. Proceedings of Machine Learning Research (vol. 97, pp. 573\u2013582). Los Angeles, United States: PMLR."},{"key":"6900_CR7","unstructured":"Berg, R. V. D., Hasenclever, L., Tomczak, J. M., & Welling, M. (2018). Sylvester normalizing flows for variational inference. In: Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence (pp. 393\u2013402). Monterey, United States: AUAI Press."},{"key":"6900_CR8","unstructured":"Bradbury, J., Frostig, R., Hawkins, P., Johnson, M. J., Leary, C., Maclaurin, D., Necula, G., Paszke, A., VanderPlas, J., Wanderman-Milne, S., & Zhang, Q. (2018). JAX: Composable transformations of Python+NumPy programs. http:\/\/github.com\/jax-ml\/jax"},{"key":"6900_CR9","unstructured":"Brofos, J., Gabri\u00e9, M., Brubaker, M. A., & Lederman, R. R. (2022). Adaptation of the independent metropolis-hastings sampler with normalizing flow proposals. In: Proceedings of The 25th International Conference on Artificial Intelligence and Statistics. Proceedings of Machine Learning Research (vol. 151, pp. 5949\u20135986). PMLR, Virtual conference."},{"key":"6900_CR10","unstructured":"Cabezas, A., & Nemeth, C. (2023). Transport elliptical slice sampling. In: Proceedings of the 26th International Conference on Artificial Intelligence and Statistics. Proceedings of Machine Learning Research (vol. 206, pp. 3664\u20133676). Valencia, Spain: PMLR."},{"key":"6900_CR11","doi-asserted-by":"publisher","first-page":"104383","DOI":"10.52202\/079017-3316","volume":"37","author":"A Cabezas","year":"2024","unstructured":"Cabezas, A., Sharrock, L., & Nemeth, C. (2024). Markovian flow matching: Accelerating MCMC with continuous normalizing flows. Advances in Neural Information Processing Systems, 37, 104383\u2013104411. Curran Associates, Inc., Vancouver, Canada.","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"4","key":"6900_CR12","doi-asserted-by":"publisher","first-page":"1747","DOI":"10.1214\/aos\/1176325754","volume":"22","author":"KS Chan","year":"1994","unstructured":"Chan, K. S., & Geyer, C. J. (1994). Discussion: Markov chains for exploring posterior distributions. Annals of Statistics, 22(4), 1747\u20131758. https:\/\/doi.org\/10.1214\/aos\/1176325754","journal-title":"Annals of Statistics"},{"key":"6900_CR13","unstructured":"Chen, R. T. Q., Behrmann, J., Duvenaud, D., & Jacobsen, J.-H. (2019). Residual flows for invertible generative modeling. Advances in Neural Information Processing Systems, 32. Curran Associates, Inc., Vancouver, Canada."},{"key":"6900_CR14","unstructured":"Cornish, R., Caterini, A., Deligiannidis, G., & Doucet, A. (2020). Relaxing bijectivity constraints with continuously indexed normalising flows. In Proceedings of the 37th International Conference on Machine Learning. Proceedings of Machine Learning Research (vol. 119, pp. 2133\u20132143). Vienna, Austria: PMLR (virtual conference)."},{"issue":"9","key":"6900_CR15","doi-asserted-by":"publisher","DOI":"10.22323\/1.396.0059","volume":"104","author":"L Del Debbio","year":"2021","unstructured":"Del Debbio, L., Marsh Rossney, J., & Wilson, M. (2021). Efficient modelling of trivializing maps for lattice $$\\phi ^4$$ theory using normalizing flows: A first look at scalability. Physical Review D, 104(9), Article 094507. https:\/\/doi.org\/10.22323\/1.396.0059","journal-title":"Physical Review D"},{"key":"6900_CR16","unstructured":"Dinh, L., Krueger, D., & Bengio, Y. (2015). NICE: Non-linear independent components estimation. arXiv:1410.8516"},{"key":"6900_CR17","unstructured":"Dinh, L., Sohl-Dickstein, J., & Bengio, S. (2017). Density estimation using Real NVP. arXiv:1605.08803"},{"key":"6900_CR18","unstructured":"Dolatabadi, H. M., Erfani, S., & Leckie, C. (2020). Invertible generative modeling using linear rational splines. In Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics. Proceedings of Machine Learning Research (vol. 108, pp. 4236\u20134246). PMLR, Virtual conference."},{"key":"6900_CR19","unstructured":"Draxler, F., Wahl, S., Schn\u00f6rr, C., & K\u00f6the, U. (2024). On the universality of volume-preserving and coupling-based normalizing flows. In: Proceedings of the 41st International Conference on Machine Learning. Proceedings of Machine Learning Research (vol. 235, pp. 11613\u201311641). Vienna, Austria: PMLR."},{"key":"6900_CR20","volume-title":"Advances in neural information processing systems","author":"C Durkan","year":"2019","unstructured":"Durkan, C., Bekasov, A., Murray, I., & Papamakarios, G., et al. (2019). Neural spline flows. In H. Wallach, H. Larochelle, A. Beygelzimer, & F. Alch\u00e9-Buc (Eds.), Advances in neural information processing systems. Vancouver: Curran Associates Inc."},{"key":"6900_CR21","unstructured":"Finlay, C., Jacobsen, J.-H., Nurbekyan, L., & Oberman, A. (2020). How to train your neural ODE: The world of Jacobian and Kinetic regularization. In: Proceedings of the 37th International Conference on Machine Learning. Proceedings of Machine Learning Research (vol. 119, pp. 3154\u20133164). Vienna, Austria: PMLR (virtual conference)."},{"issue":"10","key":"6900_CR22","doi-asserted-by":"publisher","first-page":"2109420119","DOI":"10.1073\/pnas.2109420119","volume":"119","author":"M Gabri\u00e9","year":"2022","unstructured":"Gabri\u00e9, M., Rotskoff, G. M., & Vanden-Eijnden, E. (2022). Adaptive Monte Carlo augmented with normalizing flows. Proceedings of the National Academy of Sciences, 119(10), 2109420119. https:\/\/doi.org\/10.1073\/pnas.2109420119","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"6900_CR23","unstructured":"Germain, M., Gregor, K., Murray, I., & Larochelle, H. (2015). MADE: Masked autoencoder for distribution estimation. In: Proceedings of the 32nd International Conference on Machine Learning. Proceedings of Machine Learning Research (vol. 37, pp. 881\u2013889). Lille, France: PMLR."},{"key":"6900_CR24","unstructured":"Grathwohl, W., Chen, R. T. Q., Bettencourt, J., Sutskever, I., & Duvenaud, D. (2018). FFJORD: Free-form continuous dynamics for scalable reversible generative models. arXiv. arXiv:1810.01367"},{"key":"6900_CR25","unstructured":"Grenioux, L., Durmus, A. O., Moulines, E., & Gabri\u00e9, M. (2023). On sampling with approximate transport maps. In: Proceedings of the 40th international conference on machine learning. Proceedings of Machine Learning Research (vol. 202, pp. 11698\u201311733). Honolulu, United States: PMLR."},{"key":"6900_CR26","first-page":"11629","volume":"35","author":"R Grumitt","year":"2022","unstructured":"Grumitt, R., Dai, B., & Seljak, U. (2022). Deterministic Langevin Monte Carlo with normalizing flows for Bayesian inference. Advances in Neural Information Processing Systems, 35, 11629\u201311641. Curran Associates, Inc., New Orleans, United States.","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"1","key":"6900_CR27","doi-asserted-by":"publisher","first-page":"21","DOI":"10.3390\/psf2023009021","volume":"9","author":"RDP Grumitt","year":"2024","unstructured":"Grumitt, R. D. P., Karamanis, M., & Seljak, U. (2024). Flow annealed Kalman inversion for gradient-free inference in Bayesian inverse problems. Physical Sciences Forum, 9(1), 21. https:\/\/doi.org\/10.3390\/psf2023009021","journal-title":"Physical Sciences Forum"},{"key":"6900_CR28","unstructured":"Hoffman, M. D., & Gelman, A. (2011). The no-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. arXiv:1111.4246"},{"key":"6900_CR29","unstructured":"Hoffman, M. D., Sountsov, P., Dillon, J. V., Langmore, I., Tran, D., & Vasudevan, S. (2019). NeuTra-lizing bad geometry in Hamiltonian Monte Carlo using neural transport. arXiv:1903.03704"},{"key":"6900_CR30","unstructured":"Huang, C.-W., Krueger, D., Lacoste, A., & Courville, A. (2018). Neural autoregressive flows. In: Proceedings of the 35th International Conference on Machine Learning. Proceedings of Machine Learning Research (vol. 80, pp. 2078\u20132087). Stockholm, Sweden: PMLR."},{"key":"6900_CR31","doi-asserted-by":"publisher","first-page":"1059","DOI":"10.1080\/03610919008812866","volume":"18","author":"MF Hutchinson","year":"1989","unstructured":"Hutchinson, M. F. (1989). A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines. Communication in Statistics - Simulation and Computation, 18, 1059\u20131076. https:\/\/doi.org\/10.1080\/03610919008812866","journal-title":"Communication in Statistics - Simulation and Computation"},{"issue":"2","key":"6900_CR32","doi-asserted-by":"publisher","first-page":"1644","DOI":"10.1093\/mnras\/stac2272","volume":"516","author":"M Karamanis","year":"2022","unstructured":"Karamanis, M., Beutler, F., Peacock, J. A., Nabergoj, D., & Seljak, U. (2022). Accelerating astronomical and cosmological inference with preconditioned Monte Carlo. Monthly Notices of the Royal Astronomical Society, 516(2), 1644\u20131653. Oxford University Press.","journal-title":"Monthly Notices of the Royal Astronomical Society"},{"key":"6900_CR33","unstructured":"Kingma, D. P., Salimans, T., Jozefowicz, R., Chen, X., Sutskever, I., & Welling, M. (2016). Improved variational inference with inverse autoregressive flow. Advances in Neural Information Processing Systems, 29. Curran Associates, Inc., Barcelona."},{"key":"6900_CR34","first-page":"12700","volume":"34","author":"H Lee","year":"2021","unstructured":"Lee, H., Pabbaraju, C., Sevekari, A. P., & Risteski, A. (2021). Universal approximation using well-conditioned normalizing flows. Advances in Neural Information Processing Systems, 34, 12700\u201312711.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"6900_CR35","unstructured":"Liu, Q., Lee, J. D., & Jordan, M. (2016). A kernelized stein discrepancy for goodness-of-fit tests. In: Proceedings of the 33rd International Conference on Machine Learning. Proceedings of Machine Learning Research (Vol. 48, pp. 276\u2013284). New York, United States: PMLR."},{"key":"6900_CR36","unstructured":"Magnusson, M., Torgander, J., B\u00fcrkner, P.-C., Zhang, L., Carpenter, B., & Vehtari, A. (2024). Posteriordb: Testing, benchmarking and developing Bayesian inference algorithms. arXiv. arXiv:2407.04967"},{"key":"6900_CR37","unstructured":"Matthews, A. G. D. G., Arbel, M., Rezende, D. J., & Doucet, A. (2022). Continual repeated annealed flow transport Monte Carlo. In: Proceedings of the 39th International Conference on Machine Learning. Proceedings of Machine Learning Research (vol. 162, pp. 15196\u201315219). Baltimore, United States: PMLR."},{"key":"6900_CR38","unstructured":"Midgley, L. I., Stimper, V., Simm, G. N. C., Sch\u00f6lkopf, B., & Hernandez-Lobato, J. M. (2023). Flow annealed importance sampling bootstrap. In: The Eleventh International Conference on Learning Representations, Kigali, Rwanda."},{"issue":"4","key":"6900_CR39","doi-asserted-by":"publisher","first-page":"1003","DOI":"10.1239\/jap\/1134587812","volume":"42","author":"AY Mitrophanov","year":"2005","unstructured":"Mitrophanov, A. Y. (2005). Sensitivity and convergence of uniformly ergodic Markov chains. Journal of Applied Probability, 42(4), 1003\u20131014. https:\/\/doi.org\/10.1239\/jap\/1134587812","journal-title":"Journal of Applied Probability"},{"issue":"57","key":"6900_CR40","first-page":"1","volume":"22","author":"G Papamakarios","year":"2021","unstructured":"Papamakarios, G., Nalisnick, E., Rezende, D. J., Mohamed, S., & Lakshminarayanan, B. (2021). Normalizing flows for probabilistic modeling and inference. The Journal of Machine Learning Research, 22(57), 1\u201364.","journal-title":"The Journal of Machine Learning Research"},{"key":"6900_CR41","unstructured":"Papamakarios, G., Pavlakou, T., & Murray, I. (2017). Masked autoregressive flow for density estimation. In: Advances in Neural Information Processing Systems, 30. Curran Associates, Inc., Long Beach."},{"key":"6900_CR42","first-page":"8026","volume":"32","author":"A Paszke","year":"2019","unstructured":"Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., K\u00f6pf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., \u2026 Chintala, S. (2019). PyTorch: An imperative style, high-performance deep learning library. Advances in Neural Information Processing Systems, 32, 8026\u20138037. Curran Associates Inc., Vancouver, Canada.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"6900_CR43","unstructured":"Rezende, D., & Mohamed, S. (2015). Variational inference with normalizing flows. In: Proceedings of the 32nd International Conference on Machine Learning. Proceedings of Machine Learning Research (Vol. 37, pp. 1530\u20131538). Lille, France: PMLR."},{"key":"6900_CR44","unstructured":"Salman, H., Yadollahpour, P., Fletcher, T., & Batmanghelich, K. (2018). Deep diffeomorphic normalizing flows. arXiv:1810.03256"},{"key":"6900_CR45","first-page":"5178","volume":"35","author":"S Samsonov","year":"2022","unstructured":"Samsonov, S., Lagutin, E., Gabri\u00e9, M., Durmus, A., Naumov, A., & Moulines, E. (2022). Local-global MCMC Kernels: The best of both worlds. Advances in Neural Information Processing Systems, 35, 5178\u20135193.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"6900_CR46","unstructured":"Sch\u00e4r, P., Habeck, M., & Rudolf, D. (2024). Parallel affine transformation tuning of Markov Chain Monte Carlo. In Proceedings of the 41st International Conference on Machine Learning. Proceedings of Machine Learning Research (Vol. 235, pp. 43571\u201343607). Vienna, Austria: PMLR."},{"issue":"12","key":"6900_CR47","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/ac3ae9","volume":"2021","author":"SS Schoenholz","year":"2021","unstructured":"Schoenholz, S. S., Cubuk, E. D., & Jax, M. D. (2021). A framework for differentiable physics. Journal of Statistical Mechanics: Theory and Experiment, 2021(12), Article 124016. https:\/\/doi.org\/10.1088\/1742-5468\/ac3ae9","journal-title":"Journal of Statistical Mechanics: Theory and Experiment"},{"issue":"2","key":"6900_CR48","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1002\/cpa.21423","volume":"66","author":"EG Tabak","year":"2013","unstructured":"Tabak, E. G., & Turner, C. V. (2013). A family of nonparametric density estimation algorithms. Communications on Pure and Applied Mathematics, 66(2), 145\u2013164. https:\/\/doi.org\/10.1002\/cpa.21423","journal-title":"Communications on Pure and Applied Mathematics"},{"key":"6900_CR49","doi-asserted-by":"crossref","unstructured":"Urbano, J., Lima, H., & Hanjalic, A. (2019). A new perspective on score standardization. In: Proceedings of the 42nd International ACM SIGIR Conference on Research and Development in Information Retrieval (pp. 1061\u20131064). Paris, France: Association for Computing Machinery.","DOI":"10.1145\/3331184.3331315"},{"issue":"1","key":"6900_CR50","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1145\/3147.3165","volume":"11","author":"JS Vitter","year":"1985","unstructured":"Vitter, J. S. (1985). Random sampling with a reservoir. ACM Transactions on Mathematical Software, 11(1), 37\u201357. https:\/\/doi.org\/10.1145\/3147.3165","journal-title":"ACM Transactions on Mathematical Software"},{"issue":"10","key":"6900_CR51","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.103.103006","volume":"103","author":"MJ Williams","year":"2021","unstructured":"Williams, M. J., Veitch, J., & Messenger, C. (2021). Nested sampling with normalising flows for gravitational-wave inference. Physical Review D, 103(10), Article 103006. https:\/\/doi.org\/10.1103\/PhysRevD.103.103006","journal-title":"Physical Review D"},{"key":"6900_CR52","first-page":"5933","volume":"33","author":"H Wu","year":"2020","unstructured":"Wu, H., K\u00f6hler, J., & Noe, F. (2020). Stochastic normalizing flows. Advances in Neural Information Processing Systems, 33, 5933\u20135944. Curran Associates, Inc., Vancouver, Canada (virtual conference).","journal-title":"Advances in Neural Information Processing Systems"}],"container-title":["Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-025-06900-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10994-025-06900-3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-025-06900-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T21:29:11Z","timestamp":1766438951000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10994-025-06900-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,19]]},"references-count":52,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["6900"],"URL":"https:\/\/doi.org\/10.1007\/s10994-025-06900-3","relation":{},"ISSN":["0885-6125","1573-0565"],"issn-type":[{"type":"print","value":"0885-6125"},{"type":"electronic","value":"1573-0565"}],"subject":[],"published":{"date-parts":[[2025,11,19]]},"assertion":[{"value":"18 January 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 May 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 September 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 November 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no conflict of interest to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}],"article-number":"282"}}