{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T07:58:35Z","timestamp":1773734315458,"version":"3.50.1"},"reference-count":60,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,3,24]],"date-time":"2022-03-24T00:00:00Z","timestamp":1648080000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,3,24]],"date-time":"2022-03-24T00:00:00Z","timestamp":1648080000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001663","name":"Volkswagen Foundation","doi-asserted-by":"publisher","award":["SmartStart2"],"award-info":[{"award-number":["SmartStart2"]}],"id":[{"id":"10.13039\/501100001663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000009","name":"Foundation for the National Institutes of Health","doi-asserted-by":"publisher","award":["R01 EB026949"],"award-info":[{"award-number":["R01 EB026949"]}],"id":[{"id":"10.13039\/100000009","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010304","name":"Pershing Square Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100010304","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000879","name":"Alfred P. Sloan Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000879","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100005156","name":"Alexander von Humboldt-Stiftung","doi-asserted-by":"publisher","award":["Sofja Kovalevskaja Award"],"award-info":[{"award-number":["Sofja Kovalevskaja Award"]}],"id":[{"id":"10.13039\/100005156","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Bildung und Forschung","doi-asserted-by":"publisher","award":["01IS18039B"],"award-info":[{"award-number":["01IS18039B"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat Comput Sci"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Timescales characterize the pace of change for many dynamic processes in nature. They are usually estimated by fitting the exponential decay of data autocorrelation in the time or frequency domain. Here we show that this standard procedure often fails to recover the correct timescales due to a statistical bias arising from the finite sample size. We develop an alternative approach to estimate timescales by fitting the sample autocorrelation or power spectrum with a generative model based on a mixture of Ornstein\u2013Uhlenbeck processes using adaptive approximate Bayesian computations. Our method accounts for finite sample size and noise in data and returns a posterior distribution of timescales that quantifies the estimation uncertainty and can be used for model selection. We demonstrate the accuracy of our method on synthetic data and illustrate its application to recordings from the primate cortex. We provide a customizable Python package that implements our framework via different generative models suitable for diverse applications.<\/jats:p>","DOI":"10.1038\/s43588-022-00214-3","type":"journal-article","created":{"date-parts":[[2022,3,27]],"date-time":"2022-03-27T19:03:27Z","timestamp":1648407807000},"page":"193-204","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["A flexible Bayesian framework for unbiased estimation of timescales"],"prefix":"10.1038","volume":"2","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7946-1464","authenticated-orcid":false,"given":"Roxana","family":"Zeraati","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5842-9406","authenticated-orcid":false,"given":"Tatiana A.","family":"Engel","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1355-6617","authenticated-orcid":false,"given":"Anna","family":"Levina","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,3,24]]},"reference":[{"key":"214_CR1","doi-asserted-by":"publisher","first-page":"1661","DOI":"10.1038\/nn.3862","volume":"17","author":"JD Murray","year":"2014","unstructured":"Murray, J. D. et al. A hierarchy of intrinsic timescales across primate cortex. Nat. Neurosci. 17, 1661 (2014).","journal-title":"Nat. Neurosci."},{"key":"214_CR2","doi-asserted-by":"publisher","first-page":"e42256","DOI":"10.7554\/eLife.42256","volume":"8","author":"T Watanabe","year":"2019","unstructured":"Watanabe, T., Rees, G. & Masuda, N. Atypical intrinsic neural timescale in autism. eLife 8, e42256 (2019).","journal-title":"eLife"},{"key":"214_CR3","doi-asserted-by":"publisher","first-page":"e61277","DOI":"10.7554\/eLife.61277","volume":"9","author":"R Gao","year":"2020","unstructured":"Gao, R., van den Brink, R. L., Pfeffer, T. & Voytek, B. Neuronal timescales are functionally dynamic and shaped by cortical microarchitecture. eLife 9, e61277 (2020).","journal-title":"eLife"},{"key":"214_CR4","unstructured":"Zeraati, R. et al. Attentional modulation of intrinsic timescales in visual cortex and spatial networks. Preprint at https:\/\/www.biorxiv.org\/content\/10.1101\/2021.05.17.444537v1 (2021)."},{"key":"214_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41467-018-04725-4","volume":"9","author":"J Wilting","year":"2018","unstructured":"Wilting, J. & Priesemann, V. Inferring collective dynamical states from widely unobserved systems. Nat. Commun. 9, 1\u20137 (2018).","journal-title":"Nat. Commun."},{"key":"214_CR6","doi-asserted-by":"publisher","first-page":"e18937","DOI":"10.7554\/eLife.18937","volume":"5","author":"SE Cavanagh","year":"2016","unstructured":"Cavanagh, S. E., Wallis, J. D., Kennerley, S. W. & Hunt, L. T. Autocorrelation structure at rest predicts value correlates of single neurons during reward-guided choice. eLife 5, e18937 (2016).","journal-title":"eLife"},{"key":"214_CR7","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1038\/s41586-020-03171-x","volume":"592","author":"JH Siegle","year":"2021","unstructured":"Siegle, J. H. et al. Survey of spiking in the mouse visual system reveals functional hierarchy. Nature 592, 86\u201392 (2021).","journal-title":"Nature"},{"key":"214_CR8","doi-asserted-by":"publisher","first-page":"e19695","DOI":"10.7554\/eLife.19695","volume":"5","author":"C Stringer","year":"2016","unstructured":"Stringer, C. et al. Inhibitory control of correlated intrinsic variability in cortical networks. eLife 5, e19695 (2016).","journal-title":"eLife"},{"key":"214_CR9","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1093\/cercor\/bhx321","volume":"29","author":"V Fascianelli","year":"2019","unstructured":"Fascianelli, V., Tsujimoto, S., Marcos, E. & Genovesio, A. Autocorrelation structure in the macaque dorsolateral, but not orbital or polar, prefrontal cortex predicts response-coding strength in a visually cued strategy task. Cerebral Cortex 29, 230\u2013241 (2019).","journal-title":"Cerebral Cortex"},{"key":"214_CR10","doi-asserted-by":"crossref","unstructured":"MacDowell, C. J. & Buschman, T. J. Low-dimensional spatiotemporal dynamics underlie cortex-wide neural activity. Curr. Biol. 30, 2665-2680.e8 (2020).","DOI":"10.1016\/j.cub.2020.04.090"},{"key":"214_CR11","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1038\/s41593-020-00753-w","volume":"24","author":"R Kim","year":"2021","unstructured":"Kim, R. & Sejnowski, T. J. Strong inhibitory signaling underlies stable temporal dynamics and working memory in spiking neural networks. Nat. Neurosci. 24, 129\u2013139 (2021).","journal-title":"Nat. Neurosci."},{"key":"214_CR12","doi-asserted-by":"publisher","first-page":"117141","DOI":"10.1016\/j.neuroimage.2020.117141","volume":"221","author":"T Ito","year":"2020","unstructured":"Ito, T., Hearne, L. J. & Cole, M. W. A cortical hierarchy of localized and distributed processes revealed via dissociation of task activations, connectivity changes, and intrinsic timescales. NeuroImage 221, 117141 (2020).","journal-title":"NeuroImage"},{"key":"214_CR13","doi-asserted-by":"publisher","first-page":"478","DOI":"10.1016\/S0006-3495(95)79921-0","volume":"69","author":"H Strey","year":"1995","unstructured":"Strey, H., Peterson, M. & Sackmann, E. Measurement of erythrocyte membrane elasticity by flicker eigenmode decomposition. Biophys. J. 69, 478\u2013488 (1995).","journal-title":"Biophys. J."},{"key":"214_CR14","doi-asserted-by":"crossref","unstructured":"Rohrbach, A., Meyer, T., Stelzer, E. H. & Kress, H. Measuring stepwise binding of thermally fluctuating particles to cell membranes without fluorescence. Biophys. J. 118, 1850\u20131860 (2020).","DOI":"10.1016\/j.bpj.2020.03.005"},{"key":"214_CR15","doi-asserted-by":"publisher","first-page":"e1006352","DOI":"10.1371\/journal.pcbi.1006352","volume":"15","author":"K Liu","year":"2019","unstructured":"Liu, K. et al. Hydrodynamics of transient cell\u2013cell contact: the role of membrane permeability and active protrusion length. PLoS Comput. Biol. 15, e1006352 (2019).","journal-title":"PLoS Comput. Biol."},{"key":"214_CR16","doi-asserted-by":"publisher","first-page":"1655","DOI":"10.1038\/s41593-020-00744-x","volume":"23","author":"T Donoghue","year":"2020","unstructured":"Donoghue, T. et al. Parameterizing neural power spectra into periodic and aperiodic components. Nat. Neurosci. 23, 1655\u20131665 (2020).","journal-title":"Nat. Neurosci."},{"key":"214_CR17","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1093\/biomet\/41.3-4.390","volume":"41","author":"F Marriott","year":"1954","unstructured":"Marriott, F. & Pope, J. Bias in the estimation of autocorrelations. Biometrika 41, 390\u2013402 (1954).","journal-title":"Biometrika"},{"key":"214_CR18","unstructured":"Sastry, A. S. R. Bias in estimation of serial correlation coefficients. Indian J. Stat. 11, 281\u2013296 (1951)."},{"key":"214_CR19","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1037\/0033-2909.110.2.291","volume":"110","author":"BE Huitema","year":"1991","unstructured":"Huitema, B. E. & McKean, J. W. Autocorrelation estimation and inference with small samples. Psychol. Bull. 110, 291 (1991).","journal-title":"Psychol. Bull."},{"key":"214_CR20","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1093\/biomet\/48.1-2.85","volume":"48","author":"JS White","year":"1961","unstructured":"White, J. S. Asymptotic expansions for the mean and variance of the serial correlation coefficient. Biometrika 48, 85\u201394 (1961).","journal-title":"Biometrika"},{"key":"214_CR21","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1214\/aoms\/1177707042","volume":"28","author":"Z Lomnicki","year":"1957","unstructured":"Lomnicki, Z. & Zaremba, S. On the estimation of autocorrelation in time series. Ann. Math. Stat. 28, 140\u2013158 (1957).","journal-title":"Ann. Math. Stat."},{"key":"214_CR22","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1093\/biomet\/41.3-4.403","volume":"41","author":"MG Kendall","year":"1954","unstructured":"Kendall, M. G. Note on bias in the estimation of autocorrelation. Biometrika 41, 403\u2013404 (1954).","journal-title":"Biometrika"},{"key":"214_CR23","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1016\/j.neuroimage.2019.05.011","volume":"199","author":"S Afyouni","year":"2019","unstructured":"Afyouni, S., Smith, S. M. & Nichols, T. E. Effective degrees of freedom of the pearson\u2019s correlation coefficient under autocorrelation. NeuroImage 199, 609\u2013625 (2019).","journal-title":"NeuroImage"},{"key":"214_CR24","doi-asserted-by":"crossref","first-page":"27","DOI":"10.2307\/2983611","volume":"8","author":"MS Bartlett","year":"1946","unstructured":"Bartlett, M. S. On the theoretical specification and sampling properties of autocorrelated time-series. J. R. Stat. Soc. 8, 27\u201341 (1946).","journal-title":"J. R. Stat. Soc."},{"key":"214_CR25","doi-asserted-by":"publisher","first-page":"013145","DOI":"10.1103\/PhysRevResearch.3.013145","volume":"3","author":"OM Cliff","year":"2021","unstructured":"Cliff, O. M., Novelli, L., Fulcher, B. D., Shine, J. M. & Lizier, J. T. Assessing the significance of directed and multivariate measures of linear dependence between time series. Phys. Rev. Res. 3, 013145 (2021).","journal-title":"Phys. Rev. Res."},{"key":"214_CR26","doi-asserted-by":"publisher","first-page":"604","DOI":"10.1007\/BF01449156","volume":"109","author":"A Khintchine","year":"1934","unstructured":"Khintchine, A. Korrelationstheorie der station\u00e4ren stochastischen prozesse. Math. Ann. 109, 604\u2013615 (1934).","journal-title":"Math. Ann."},{"key":"214_CR27","doi-asserted-by":"publisher","first-page":"062142","DOI":"10.1103\/PhysRevE.100.062142","volume":"100","author":"HH Strey","year":"2019","unstructured":"Strey, H. H. Estimation of parameters from time traces originating from an Ornstein\u2013Uhlenbeck process. Phys. Rev. E 100, 062142 (2019).","journal-title":"Phys. Rev. E"},{"key":"214_CR28","doi-asserted-by":"crossref","unstructured":"Spitmaan, M. M., Seo, H., Lee, D. & Soltani, A. Multiple timescales of neural dynamics and integration of task-relevant signals across cortex. Proc. Natl Acad. Sci. USA 117, 22522\u201322531 (2020).","DOI":"10.1073\/pnas.2005993117"},{"key":"214_CR29","doi-asserted-by":"publisher","first-page":"3345","DOI":"10.1152\/jn.1998.80.6.3345","volume":"80","author":"CD Brody","year":"1998","unstructured":"Brody, C. D. Slow covariations in neuronal resting potentials can lead to artefactually fast cross-correlations in their spike trains. J. Neurophysiol. 80, 3345\u20133351 (1998).","journal-title":"J. Neurophysiol."},{"key":"214_CR30","doi-asserted-by":"publisher","first-page":"2928","DOI":"10.1152\/jn.00644.2004","volume":"94","author":"V Ventura","year":"2005","unstructured":"Ventura, V., Cai, C. & Kass, R. E. Trial-to-trial variability and its effect on time-varying dependency between two neurons. J. Neurophysiol. 94, 2928\u20132939 (2005).","journal-title":"J. Neurophysiol."},{"key":"214_CR31","doi-asserted-by":"publisher","first-page":"517","DOI":"10.1152\/jn.00633.2011","volume":"107","author":"A Amarasingham","year":"2012","unstructured":"Amarasingham, A., Harrison, M. T., Hatsopoulos, N. G. & Geman, S. Conditional modeling and the jitter method of spike resampling. J. Neurophysiol. 107, 517\u2013531 (2012).","journal-title":"J. Neurophysiol."},{"key":"214_CR32","doi-asserted-by":"publisher","first-page":"811","DOI":"10.1038\/nn.2842","volume":"14","author":"MR Cohen","year":"2011","unstructured":"Cohen, M. R. & Kohn, A. Measuring and interpreting neuronal correlations. Nat. Neurosci. 14, 811 (2011).","journal-title":"Nat. Neurosci."},{"key":"214_CR33","doi-asserted-by":"publisher","first-page":"983","DOI":"10.1093\/biomet\/asp052","volume":"96","author":"MA Beaumont","year":"2009","unstructured":"Beaumont, M. A., Cornuet, J.-M., Marin, J.-M. & Robert, C. P. Adaptive approximate bayesian computation. Biometrika 96, 983\u2013990 (2009).","journal-title":"Biometrika"},{"key":"214_CR34","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1007\/s10827-009-0208-9","volume":"29","author":"RC Kelly","year":"2010","unstructured":"Kelly, R. C., Smith, M. A., Kass, R. E. & Lee, T. S. Local field potentials indicate network state and account for neuronal response variability. J. Comput. Neurosci. 29, 567\u2013579 (2010).","journal-title":"J. Comput. Neurosci."},{"key":"214_CR35","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/j.neuron.2014.02.006","volume":"82","author":"AS Ecker","year":"2014","unstructured":"Ecker, A. S. et al. State dependence of noise correlations in macaque primary visual cortex. Neuron 82, 235\u2013248 (2014).","journal-title":"Neuron"},{"key":"214_CR36","doi-asserted-by":"publisher","first-page":"674","DOI":"10.1038\/s42256-020-00242-6","volume":"2","author":"M Genkin","year":"2020","unstructured":"Genkin, M. & Engel, T. A. Moving beyond generalization to accurate interpretation of flexible models. Nat. Mach. Intell. 2, 674\u2013683 (2020).","journal-title":"Nat. Mach. Intell."},{"key":"214_CR37","doi-asserted-by":"crossref","unstructured":"Neophytou, D., Arribas, D., Levy, R., Park, I. M. & Oviedo, H. V. Recurrent connectivity underlies lateralized temporal processing differences in auditory cortex. Preprint at https:\/\/www.biorxiv.org\/content\/10.1101\/2021.04.14.439872v1 (2021).","DOI":"10.1101\/2021.04.14.439872"},{"key":"214_CR38","doi-asserted-by":"publisher","first-page":"1555","DOI":"10.1109\/TBME.2014.2311996","volume":"61","author":"B Babadi","year":"2014","unstructured":"Babadi, B. & Brown, E. N. A review of multitaper spectral analysis. IEEE Trans. Biomed. Eng. 61, 1555\u20131564 (2014).","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"214_CR39","doi-asserted-by":"publisher","first-page":"058101","DOI":"10.1103\/PhysRevLett.94.058101","volume":"94","author":"C Haldeman","year":"2005","unstructured":"Haldeman, C. & Beggs, J. M. Critical branching captures activity in living neural networks and maximizes the number of metastable states. Phys. Rev. Lett. 94, 058101 (2005).","journal-title":"Phys. Rev. Lett."},{"key":"214_CR40","doi-asserted-by":"publisher","first-page":"022301","DOI":"10.1103\/PhysRevE.101.022301","volume":"101","author":"J Zierenberg","year":"2020","unstructured":"Zierenberg, J., Wilting, J., Priesemann, V. & Levina, A. Description of spreading dynamics by microscopic network models and macroscopic branching processes can differ due to coalescence. Phys. Rev. E 101, 022301 (2020).","journal-title":"Phys. Rev. E"},{"key":"214_CR41","doi-asserted-by":"publisher","first-page":"013115","DOI":"10.1103\/PhysRevResearch.2.013115","volume":"2","author":"J Zierenberg","year":"2020","unstructured":"Zierenberg, J., Wilting, J., Priesemann, V. & Levina, A. Tailored ensembles of neural networks optimize sensitivity to stimulus statistics. Phys. Rev. Res. 2, 013115 (2020).","journal-title":"Phys. Rev. Res."},{"key":"214_CR42","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1214\/09-BA412","volume":"4","author":"A Grelaud","year":"2009","unstructured":"Grelaud, A. et al. ABC likelihood-free methods for model choice in gibbs random fields. Bayesian Anal. 4, 317\u2013335 (2009).","journal-title":"Bayesian Anal."},{"key":"214_CR43","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1214\/11-BA602","volume":"6","author":"X Didelot","year":"2011","unstructured":"Didelot, X., Everitt, R. G., Johansen, A. M. & Lawson, D. J. et al. Likelihood-free estimation of model evidence. Bayesian Anal. 6, 49\u201376 (2011).","journal-title":"Bayesian Anal."},{"key":"214_CR44","doi-asserted-by":"crossref","unstructured":"Marin, J.-M., Pillai, N. S., Robert, C. P. & Rousseau, J. Relevant statistics for Bayesian model choice. J. R. Stat. Soc. B 76, 833\u2013859 (2014).","DOI":"10.1111\/rssb.12056"},{"key":"214_CR45","doi-asserted-by":"publisher","first-page":"15112","DOI":"10.1073\/pnas.1102900108","volume":"108","author":"CP Robert","year":"2011","unstructured":"Robert, C. P., Cornuet, J.-M., Marin, J.-M. & Pillai, N. S. Lack of confidence in approximate Bayesian computation model choice. Proc. Natl Acad. Sci. USA 108, 15112\u201315117 (2011).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"214_CR46","unstructured":"Bishop, C. M. Pattern Recognition and Machine Learning (Springer, 2006)."},{"key":"214_CR47","doi-asserted-by":"publisher","first-page":"1140","DOI":"10.1126\/science.aag1420","volume":"354","author":"TA Engel","year":"2016","unstructured":"Engel, T. A. et al. Selective modulation of cortical state during spatial attention. Science 354, 1140\u20131144 (2016).","journal-title":"Science"},{"key":"214_CR48","doi-asserted-by":"publisher","first-page":"818","DOI":"10.1016\/j.neuron.2010.12.037","volume":"69","author":"AK Churchland","year":"2011","unstructured":"Churchland, A. K. et al. Variance as a signature of neural computations during decision making. Neuron 69, 818\u2013831 (2011).","journal-title":"Neuron"},{"key":"214_CR49","doi-asserted-by":"publisher","first-page":"858","DOI":"10.1038\/nn.3711","volume":"17","author":"RL Goris","year":"2014","unstructured":"Goris, R. L., Movshon, J. A. & Simoncelli, E. P. Partitioning neuronal variability. Nat. Neurosci. 17, 858 (2014).","journal-title":"Nat. Neurosci."},{"key":"214_CR50","doi-asserted-by":"publisher","first-page":"1537","DOI":"10.1162\/089976699300016133","volume":"11","author":"CD Brody","year":"1999","unstructured":"Brody, C. D. Correlations without synchrony. Neural Comput. 11, 1537\u20131551 (1999).","journal-title":"Neural Comput."},{"key":"214_CR51","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.neuroimage.2017.06.078","volume":"158","author":"R Gao","year":"2017","unstructured":"Gao, R., Peterson, E. J. & Voytek, B. Inferring synaptic excitation\/inhibition balance from field potentials. Neuroimage 158, 70\u201378 (2017).","journal-title":"Neuroimage"},{"key":"214_CR52","doi-asserted-by":"publisher","first-page":"579","DOI":"10.3758\/BF03196615","volume":"11","author":"E-J Wagenmakers","year":"2004","unstructured":"Wagenmakers, E.-J., Farrell, S. & Ratcliff, R. Estimation and interpretation of 1\/f \u03b1 noise in human cognition. Psych. Bull. Rev. 11, 579\u2013615 (2004).","journal-title":"Psych. Bull. Rev."},{"key":"214_CR53","doi-asserted-by":"publisher","first-page":"823","DOI":"10.1103\/PhysRev.36.823","volume":"36","author":"GE Uhlenbeck","year":"1930","unstructured":"Uhlenbeck, G. E. & Ornstein, L. S. On the theory of the Brownian motion. Phys. Rev. 36, 823 (1930).","journal-title":"Phys. Rev."},{"key":"214_CR54","doi-asserted-by":"crossref","unstructured":"Risken, H. in The Fokker\u2013Planck Equation 63\u201395 (Springer, 1996).","DOI":"10.1007\/978-3-642-61544-3_4"},{"key":"214_CR55","doi-asserted-by":"crossref","unstructured":"Lindner, B. in Stochastic Methods in Neuroscience Vol. 1 (Oxford Univ. Press, 2009).","DOI":"10.1093\/acprof:oso\/9780199235070.003.0001"},{"key":"214_CR56","doi-asserted-by":"crossref","unstructured":"Sunn\u00e5ker, M. et al. Approximate Bayesian computation. PLoS Comput. Biol. 9, e1002803 (2013).","DOI":"10.1371\/journal.pcbi.1002803"},{"key":"214_CR57","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1093\/bioinformatics\/btp619","volume":"26","author":"T Toni","year":"2010","unstructured":"Toni, T. & Stumpf, M. P. Simulation-based model selection for dynamical systems in systems and population biology. Bioinformatics 26, 104\u2013110 (2010).","journal-title":"Bioinformatics"},{"key":"214_CR58","doi-asserted-by":"publisher","unstructured":"Zeraati, R., Engel, T. A. & Levina, A. Roxana-zeraati\/abcTau: A flexible Bayesian Framework for Unbiased Estimation of Timescales (Zenodo, 2022); https:\/\/doi.org\/10.5281\/zenodo.5949117","DOI":"10.5281\/zenodo.5949117"},{"key":"214_CR59","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1037\/0033-2909.111.2.361","volume":"111","author":"KO McGraw","year":"1992","unstructured":"McGraw, K. O. & Wong, S. P. A common language effect size statistic. Psychol. Bull. 111, 361 (1992).","journal-title":"Psychol. Bull."},{"key":"214_CR60","doi-asserted-by":"publisher","unstructured":"Steinmetz, N. & Moore, T. Dataset of Linear-Array Recordings From Macaque V4 During a Fixation Task (Figshare, 2022); https:\/\/doi.org\/10.6084\/m9.figshare.19077875.v1","DOI":"10.6084\/m9.figshare.19077875.v1"}],"container-title":["Nature Computational Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s43588-022-00214-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s43588-022-00214-3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s43588-022-00214-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T22:27:16Z","timestamp":1726871236000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s43588-022-00214-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,24]]},"references-count":60,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["214"],"URL":"https:\/\/doi.org\/10.1038\/s43588-022-00214-3","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2020.08.11.245944","asserted-by":"object"}]},"ISSN":["2662-8457"],"issn-type":[{"value":"2662-8457","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,24]]},"assertion":[{"value":"25 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 February 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}