{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T07:39:04Z","timestamp":1772350744275,"version":"3.50.1"},"reference-count":85,"publisher":"Springer Science and Business Media LLC","issue":"1","funder":[{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Bildung und Forschung","doi-asserted-by":"crossref","award":["01ZX1310B"],"award-info":[{"award-number":["01ZX1310B"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Syst Biol"],"published-print":{"date-parts":[[2017,12]]},"DOI":"10.1186\/s12918-017-0433-1","type":"journal-article","created":{"date-parts":[[2017,6,24]],"date-time":"2017-06-24T10:27:33Z","timestamp":1498300053000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["Comprehensive benchmarking of Markov chain Monte Carlo methods for dynamical systems"],"prefix":"10.1186","volume":"11","author":[{"given":"Benjamin","family":"Ballnus","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sabine","family":"Hug","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kathrin","family":"Hatz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linus","family":"G\u00f6rlitz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"Hasenauer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fabian J.","family":"Theis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,6,24]]},"reference":[{"issue":"1","key":"433_CR1","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1186\/s12918-015-0219-2","volume":"9","author":"A G\u00e1bor","year":"2015","unstructured":"G\u00e1bor A, Banga JR. Robust and efficient parameter estimation in dynamic models of biological systems. BMC Syst Biol. 2015; 9(1):74.","journal-title":"BMC Syst Biol"},{"issue":"8","key":"433_CR2","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1038\/nbt1114","volume":"23","author":"E Klipp","year":"2005","unstructured":"Klipp E, Nordlander B, Kr\u00fcger R, Gennemark P, Hohmann S. Integrative model of the response of yeast to osmotic shock. Nat Biotechnol. 2005; 23(8):975\u201382.","journal-title":"Nat Biotechnol"},{"issue":"6912","key":"433_CR3","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1038\/nature01254","volume":"420","author":"H Kitano","year":"2002","unstructured":"Kitano H. Computational systems biology. Nature. 2002; 420(6912):206\u201310.","journal-title":"Nature"},{"issue":"1984","key":"433_CR4","doi-asserted-by":"crossref","first-page":"20110544","DOI":"10.1098\/rsta.2011.0544","volume":"371","author":"A Raue","year":"2013","unstructured":"Raue A, Kreutz C, Theis FJ, Timmer J. Joining forces of Bayesian and Frequentist methodology: a study for inference in the presence of non-identifiability. Phil Trans R Soc A Math Phys Eng Sci. 2013; 371(1984):20110544.","journal-title":"Phil Trans R Soc A Math Phys Eng Sci"},{"issue":"2","key":"433_CR5","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.mbs.2013.04.002","volume":"246","author":"S Hug","year":"2013","unstructured":"Hug S, Raue A, Hasenauer J, Bachmann J, Klingm\u00fcller U, Timmer J, Theis FJ. High-dimensional bayesian parameter estimation: case study for a model of JAK2\/STAT5 signaling. Math Biosci. 2013; 246(2):293\u2013304.","journal-title":"Math Biosci"},{"key":"433_CR6","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1016\/j.ymben.2006.04.003","volume":"8","author":"M Joshi","year":"2006","unstructured":"Joshi M, Seidel-Morgenstern A, Kremling A. Exploiting the bootstrap method for quantifying parameter confidence intervals in dynamical systems. Metab Engeneering. 2006; 8:447\u201355.","journal-title":"Metab Engeneering"},{"key":"433_CR7","volume-title":"Proceedings of the 12th International Conference on Computational Methods in Systems Biology (CMSB 2014), Lecture Notes in Bioinformatics","author":"F Fr\u00f6hlich","year":"2014","unstructured":"Fr\u00f6hlich F, Theis FJ, Hasenauer J. Uncertainty analysis for non-identifiable dynamical systems: Profile likelihoods, bootstrapping and more. In: Mendes P, Dada JO, Smallbone KO, editors. Proceedings of the 12th International Conference on Computational Methods in Systems Biology (CMSB 2014), Lecture Notes in Bioinformatics. Manchester: Springer: 2014. p. 61\u201372."},{"issue":"15","key":"433_CR8","doi-asserted-by":"crossref","first-page":"1923","DOI":"10.1093\/bioinformatics\/btp358","volume":"25","author":"A Raue","year":"2009","unstructured":"Raue A, Kreutz C, Maiwald T, Bachmann J, Schilling M, Klingm\u00fcller U, Timmer J. Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics. 2009; 25(15):1923\u20139.","journal-title":"Bioinformatics"},{"issue":"2","key":"433_CR9","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1093\/bib\/bbm007","volume":"8","author":"DJ Wilkinson","year":"2007","unstructured":"Wilkinson DJ. Bayesian methods in bioinformatics and computational systems biology. Brief Bioinform. 2007; 8(2):109\u201316.","journal-title":"Brief Bioinform"},{"issue":"113","key":"433_CR10","first-page":"20","volume":"3","author":"TR Xu","year":"2010","unstructured":"Xu TR, Vyshemirsky V, Gormand A, et al. Inferring signaling pathway topologies from multiple perturbation measurements of specific biochemical species. Sci Signal. 2010; 3(113):20.","journal-title":"Sci Signal"},{"issue":"6","key":"433_CR11","first-page":"1","volume":"1","author":"M Krauss","year":"2013","unstructured":"Krauss M, Burghaus R, Lippert J, Niemi M, Neuvonen P, Schuppert A, Willmann S, Kuepfer L, G\u00f6rlitz L. Using Bayesian-PBPK modeling for assessment of inter-individual variability and subgroup stratification. In Silico Pharmacol. 2013; 1(6):1\u201311.","journal-title":"In Silico Pharmacol"},{"issue":"9","key":"433_CR12","doi-asserted-by":"crossref","first-page":"74335","DOI":"10.1371\/journal.pone.0074335","volume":"8","author":"A Raue","year":"2013","unstructured":"Raue A, Schilling M, Bachmann J, Matteson A, Schelker M, Schelke M, Kaschek D, Hug S, Kreutz C, Harms BD, Theis FJ, Klingm\u00fcller U, Timmer J. Lessons learned from quantitative dynamical modeling in systems biology. PloS ONE. 2013; 8(9):74335.","journal-title":"PloS ONE"},{"issue":"25","key":"433_CR13","doi-asserted-by":"crossref","first-page":"1923","DOI":"10.1093\/bioinformatics\/btp358","volume":"25","author":"A Raue","year":"2009","unstructured":"Raue A, Kreutz C, Maiwald T, Bachmann J, Schilling M, Klingm\u00fcller U, Timmer J. Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinf. 2009; 25(25):1923\u20139.","journal-title":"Bioinf"},{"key":"433_CR14","doi-asserted-by":"crossref","unstructured":"Balsa-Canto E, Alonso AA, Banga JR. An iterative identification procedure for dynamic modeling of biochemical networks. BMC Syst Biol. 2010; 4:11. http:\/\/bmcsystbiol.biomedcentral.com\/articles\/10.1186\/1752-0509-4-11 .","DOI":"10.1186\/1752-0509-4-11"},{"issue":"18","key":"433_CR15","doi-asserted-by":"crossref","first-page":"2610","DOI":"10.1093\/bioinformatics\/btr431","volume":"27","author":"O Chi\u015f","year":"2011","unstructured":"Chi\u015f O, Banga JR, Balsa-Canto E. GenSSI: a software toolbox for structural identifiability analysis of biological models. Bioinformatics. 2011; 27(18):2610\u201311.","journal-title":"Bioinformatics"},{"key":"433_CR16","volume-title":"Proc. of the 18th IFAC World Congress, vol. 18","author":"P Weber","year":"2011","unstructured":"Weber P, Hasenauer J, Allg\u00f6wer F, Radde N. Parameter estimation and identifiability of biological networks using relative data. In: Bittanti S, Cenedese A, Zampieri S, editors. Proc. of the 18th IFAC World Congress, vol. 18. Milano: Elsevier: 2011. p. 11648\u201353."},{"issue":"6767","key":"433_CR17","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1038\/35002131","volume":"403","author":"T Gardner","year":"2000","unstructured":"Gardner T, Cantor C, Collins J. Construction of a genetic toggle switch in escherichia coli. Nature. 2000; 403(6767):242\u2013339.","journal-title":"Nature"},{"issue":"6976","key":"433_CR18","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1038\/nature02298","volume":"427","author":"EM Ozbudak","year":"2004","unstructured":"Ozbudak EM, Thattai M, Lim HN, Shraiman BI, van Oudenaarden A. Multistability in the lactose utilization network of Escherichia coli. Nature. 2004; 427(6976):737\u201340.","journal-title":"Nature"},{"key":"433_CR19","doi-asserted-by":"crossref","first-page":"7328","DOI":"10.1073\/pnas.88.16.7328","volume":"88","author":"JJ Tyson","year":"1991","unstructured":"Tyson JJ. Modeling the cell division cycle: cdc2 and cyclin interactions. Proc Nati Acad Sci USA. 1991; 88:7328\u201332.","journal-title":"Proc Nati Acad Sci USA"},{"issue":"6","key":"433_CR20","doi-asserted-by":"crossref","first-page":"1583","DOI":"10.1046\/j.1432-1327.2000.01197.x","volume":"267","author":"BN Kholodenko","year":"2000","unstructured":"Kholodenko BN. Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades. Eur J Biochem. 2000; 267(6):1583\u20138.","journal-title":"Eur J Biochem"},{"key":"433_CR21","unstructured":"Calderhead B. A study of population MCMC for estimating Bayes factors over nonlinear ODE models. Master thesis, University of Glasgow. 2007."},{"issue":"28","key":"433_CR22","doi-asserted-by":"crossref","first-page":"9823","DOI":"10.1073\/pnas.0803499105","volume":"105","author":"S Kosuta","year":"2008","unstructured":"Kosuta S, Hazledine S, Sun J, Miwa H, Morris RJ, Downie JA, Oldroyd GE. Differential and chaotic calcium signatures in the symbiosis signaling pathway of legumes. Proc Natl Acad Sci. 2008; 105(28):9823\u201328.","journal-title":"Proc Natl Acad Sci"},{"issue":"3","key":"433_CR23","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/s12080-016-0293-0","volume":"9","author":"CN Ngonghala","year":"2016","unstructured":"Ngonghala CN, Teboh-Ewungkem MI, Ngwa GA. Observance of period-doubling bifurcation and chaos in an autonomous ODE model for malaria with vector demography. Theor Ecol. 2016; 9(3):337\u201351.","journal-title":"Theor Ecol"},{"issue":"4","key":"433_CR24","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1002\/(SICI)1097-0134(199712)29:4<417::AID-PROT2>3.0.CO;2-5","volume":"29","author":"M Braxenthaler","year":"1997","unstructured":"Braxenthaler M, Unger R, Auerbach D, Given JA, Moult J. Chaos in protein dynamics. Protein Struct Funct Genet. 1997; 29(4):417\u201325.","journal-title":"Protein Struct Funct Genet"},{"key":"433_CR25","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1186\/s12918-015-0144-4","volume":"9","author":"AF Villaverde","year":"2015","unstructured":"Villaverde AF, Henriques D, Smallbone K, Bongard S, Schmid J, Cicin-Sain D, Crombach A, Saez-Rodriguez J, Mauch K, Balsa-Canto E, et al. BioPreDyn-bench: a suite of benchmark problems for dynamic modelling in systems biology. BMC Syst Biol. 2015; 9:8.","journal-title":"BMC Syst Biol"},{"key":"433_CR26","volume-title":"The EvA2 Optimization Framework","author":"M Kronfeld","year":"2010","unstructured":"Kronfeld M, Planatscher H, Zell A. The EvA2 Optimization Framework. Berlin: Springer; 2010."},{"key":"433_CR27","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1186\/1471-2105-15-136","volume":"15","author":"JA Egea","year":"2014","unstructured":"Egea JA, Henriques D, Cokelaer T, Villaverde AF, MacNamara A, Danciu DP, Banga JR, Saez-Rodriguez J. MEIGO: an open-source software suite based on metaheuristics for global optimization in systems biology and bioinformatics. BMC Bioinforma. 2014; 15:136.","journal-title":"BMC Bioinforma"},{"issue":"4","key":"433_CR28","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/s11222-006-9438-0","volume":"16","author":"H Haario","year":"2006","unstructured":"Haario H, Laine M, Mira A, Saksman E. DRAM: efficient adaptive MCMC. Statistics and Computing. 2006; 16(4):339\u201354.","journal-title":"Statistics and Computing"},{"issue":"2","key":"433_CR29","doi-asserted-by":"crossref","first-page":"223","DOI":"10.2307\/3318737","volume":"7","author":"H Haario","year":"2001","unstructured":"Haario H, Saksman E, Tamminen J. An adaptive Metropolis algorithm. Bernoulli. 2001; 7(2):223\u201342.","journal-title":"Bernoulli"},{"issue":"2","key":"433_CR30","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1198\/jcgs.2009.06134","volume":"18","author":"GO Roberts","year":"2009","unstructured":"Roberts GO, Rosenthal JS. Examples of adaptive MCMC. J Comput Graph Stat. 2009; 18(2):349\u201367.","journal-title":"J Comput Graph Stat"},{"issue":"4","key":"433_CR31","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s11222-008-9110-y","volume":"18","author":"C Andrieu","year":"2008","unstructured":"Andrieu C, Thoms J. A tutorial on adaptive MCMC. Stat Comput. 2008; 18(4):343\u201373.","journal-title":"Stat Comput"},{"key":"433_CR32","first-page":"1","volume":"26","author":"MK Lacki","year":"2015","unstructured":"Lacki MK, Miasojedow B. State-dependent swap strategies and automatic reduction of number of temperatures in adaptive parallel tempering algorithm. Stat Comput. 2015; 26:1\u201314.","journal-title":"Stat Comput"},{"key":"433_CR33","first-page":"342","volume":"196","author":"M Sambridge","year":"2013","unstructured":"Sambridge M. A parallel tempering algorithm for probabilistic sampling and multimodal optimization. Geophys J Int. 2013; 196:342.","journal-title":"Geophys J Int"},{"issue":"3","key":"433_CR34","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1080\/10618600.2013.778779","volume":"22","author":"B Miasojedow","year":"2013","unstructured":"Miasojedow B, Moulines E, Vihola M. An adaptive parallel tempering algorithm. J Comput Graph Stat. 2013; 22(3):649\u201364.","journal-title":"J Comput Graph Stat"},{"issue":"2","key":"433_CR35","doi-asserted-by":"crossref","first-page":"1919","DOI":"10.1093\/mnras\/stv2422","volume":"455","author":"W Vousden","year":"2016","unstructured":"Vousden W, Farr WM, Mandel I. Dynamic temperature selection for parallel tempering in Markov chain Monte Carlo simulations. Mon Not R Astron Soc. 2016; 455(2):1919\u201337.","journal-title":"Mon Not R Astron Soc"},{"issue":"6","key":"433_CR36","doi-asserted-by":"crossref","first-page":"1450","DOI":"10.1016\/j.csda.2011.11.020","volume":"56","author":"F Rigat","year":"2012","unstructured":"Rigat F, Mira A. Parallel hierarchical sampling: A general-purpose interacting Markov chains Monte Carlo algorithm. Comput Stat Data Anal. 2012; 56(6):1450\u201367.","journal-title":"Comput Stat Data Anal"},{"issue":"2","key":"433_CR37","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1111\/j.1467-9868.2010.00765.x","volume":"73","author":"M Girolami","year":"2011","unstructured":"Girolami M, Calderhead B. Riemann manifold Langevin and Hamiltonian Monte Carlo methods. J R Stat Soc Ser B (Stat Methodol). 2011; 73(2):123\u2013214.","journal-title":"J R Stat Soc Ser B (Stat Methodol)"},{"key":"433_CR38","doi-asserted-by":"crossref","DOI":"10.1002\/3527603603","volume-title":"Systems Biology in Practice","author":"E Klipp","year":"2005","unstructured":"Klipp E, Herwig R, Kowald A, Wierling C, Lehrach H. Systems Biology in Practice. Weinheim: Wiley-VCH; 2005."},{"issue":"1-2","key":"433_CR39","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1020281327116","volume":"50","author":"C Andrieu","year":"2003","unstructured":"Andrieu C, De Freitas N, Doucet A, Jordan MI. An introduction to MCMC for machine learning. Mach Learn. 2003; 50(1-2):5\u201343.","journal-title":"Mach Learn"},{"issue":"6","key":"433_CR40","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1063\/1.1699114","volume":"21","author":"N Metropolis","year":"1953","unstructured":"Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E. Equation of state calculations by fast computing machines. J Chem Phys. 1953; 21(6):1087\u201392.","journal-title":"J Chem Phys"},{"issue":"1","key":"433_CR41","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1093\/biomet\/57.1.97","volume":"57","author":"WK Hastings","year":"1970","unstructured":"Hastings WK. Monte Carlo sampling methods using Markov chains and their applications. Biometrika. 1970; 57(1):97\u2013109.","journal-title":"Biometrika"},{"key":"433_CR42","unstructured":"Calderhead B. Differential geometric MCMC methods and applications. PhD thesis, University of Glasgow. 2011."},{"issue":"10","key":"433_CR43","doi-asserted-by":"crossref","first-page":"1440","DOI":"10.1093\/bioinformatics\/btu006","volume":"30","author":"A Raue","year":"2014","unstructured":"Raue A, Karlsson J, Saccomani MP, Jirstrand M, Timmer J. Comparison of approaches for parameter identifiability analysis of biological systems. Bioinformatics. 2014; 30(10):1440\u201348.","journal-title":"Bioinformatics"},{"issue":"4","key":"433_CR44","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1023\/A:1008820505350","volume":"8","author":"SP Brooks","year":"1998","unstructured":"Brooks SP, Roberts GO. Assessing convergence of Markov chain Monte Carlo algorithms. Stat Comput. 1998; 8(4):319\u201335.","journal-title":"Stat Comput"},{"key":"433_CR45","first-page":"169","volume":"4","author":"J Geweke","year":"1992","unstructured":"Geweke J. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. Bayesian Stat. 1992; 4:169\u201388.","journal-title":"Bayesian Stat"},{"issue":"2","key":"433_CR46","first-page":"65","volume":"6","author":"S Holm","year":"1979","unstructured":"Holm S. A simple sequentially rejective multiple test procedure. Scand J Stat. 1979; 6(2):65\u201370.","journal-title":"Scand J Stat"},{"issue":"4","key":"433_CR47","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1080\/10618600.1998.10474787","volume":"7","author":"SP Brooks","year":"1998","unstructured":"Brooks SP, Gelman A. General methods for monitoring convergence of iterative simulations. J Comput Graph Stat. 1998; 7(4):434\u201355.","journal-title":"J Comput Graph Stat"},{"issue":"1","key":"433_CR48","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1214\/13-BA801","volume":"8","author":"D Schmidl","year":"2013","unstructured":"Schmidl D, Czado C, Hug S, Theis FJ, et al. A vine-copula based adaptive MCMC sampler for efficient inference of dynamical systems. Bayesian Anal. 2013; 8(1):1\u201322.","journal-title":"Bayesian Anal"},{"issue":"1","key":"433_CR49","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1109\/78.651165","volume":"46","author":"MD Sacchi","year":"1998","unstructured":"Sacchi MD, Ulrych TJ, Walker CJ. Interpolation and extrapolation using a high-resolution discrete Fourier transform. IEEE Trans Signal Process. 1998; 46(1):31\u20138.","journal-title":"IEEE Trans Signal Process"},{"issue":"4","key":"433_CR50","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1016\/j.nano.2013.11.008","volume":"10","author":"C Leonhardt","year":"2014","unstructured":"Leonhardt C, Schwake G, St\u00f6gbauer TR, Rappl S, Kuhr JT, Ligon TS, R\u00e4dler JO. Single-cell mRNA transfection studies: delivery, kinetics and statistics by numbers. Nanomedicine Nanotechnol Biol Med. 2014; 10(4):679\u201388.","journal-title":"Nanomedicine Nanotechnol Biol Med"},{"issue":"1","key":"433_CR51","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1186\/1752-0509-3-90","volume":"3","author":"T Wilhelm","year":"2009","unstructured":"Wilhelm T. The smallest chemical reaction system with bistability. BMC Syst Biol. 2009; 3(1):90.","journal-title":"BMC Syst Biol"},{"key":"433_CR52","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1109\/TAC.2007.911328","volume":"53","author":"M Chaves","year":"2008","unstructured":"Chaves M, Eissing T, Allg\u00f6wer F. Bistable biological systems: A characterization through local compact input-to-state stability. IEEE Trans Autom Control. 2008; 53:87\u2013100.","journal-title":"IEEE Trans Autom Control"},{"key":"433_CR53","volume-title":"Bifurcations Involving Fixed Points and Limit Cycles in Biological Systems","author":"MR Guevara","year":"2003","unstructured":"Guevara MR. Bifurcations Involving Fixed Points and Limit Cycles in Biological Systems. New York: Springer; 2003."},{"issue":"1","key":"433_CR54","doi-asserted-by":"crossref","first-page":"779","DOI":"10.15252\/msb.20145352","volume":"11","author":"AE Sgro","year":"2015","unstructured":"Sgro AE, Schwab DJ, Noorbakhsh J, Mestler T, Mehta P, Gregor T. From intracellular signaling to population oscillations: bridging size- and time-scales in collective behavior. Mol Syst Biol. 2015; 11(1):779.","journal-title":"Mol Syst Biol"},{"issue":"2","key":"433_CR55","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1049\/iet-syb.2014.0010","volume":"9","author":"C Zimmer","year":"2015","unstructured":"Zimmer C, Sahle S, Pahle J. Exploiting intrinsic fluctuations to identify model parameters. IET Syst Biol. 2015; 9(2):64\u201373.","journal-title":"IET Syst Biol"},{"issue":"3","key":"433_CR56","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1214\/12-BA724","volume":"7","author":"A Solonen","year":"2012","unstructured":"Solonen A, Ollinaho P, Laine M, Haario H, Tamminen J, J\u00e4rvinen H, et al. Efficient MCMC for climate model parameter estimation: Parallel adaptive chains and early rejection. Bayesian Anal. 2012; 7(3):715\u201336.","journal-title":"Bayesian Anal"},{"issue":"2","key":"433_CR57","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1529\/biophysj.107.126086","volume":"95","author":"PD Kirk","year":"2008","unstructured":"Kirk PD, Toni T, Stumpf MP. Parameter inference for biochemical systems that undergo a Hopf bifurcation. Biophys J. 2008; 95(2):540\u20139.","journal-title":"Biophys J"},{"issue":"4","key":"433_CR58","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1103\/RevModPhys.63.991","volume":"63","author":"JD Crawford","year":"1991","unstructured":"Crawford JD. Introduction to bifurcation theory. Rev Mod Phys. 1991; 63(4):991.","journal-title":"Rev Mod Phys"},{"key":"433_CR59","volume-title":"Elements of Applied Bifurcation Theory.","author":"YA Kuznetsov","year":"2013","unstructured":"Kuznetsov YA. Elements of Applied Bifurcation Theory.New York: Springer; 2013."},{"key":"433_CR60","doi-asserted-by":"crossref","unstructured":"Dercole F, Rinaldi S. Dynamical systems and their bifurcations. Hoboken: Wiley; 2011. pp. 291\u2013325. doi: 10.1002\/9781118007747.ch12 . http:\/\/dx.doi.org\/10.1002\/9781118007747.ch12","DOI":"10.1002\/9781118007747.ch12"},{"issue":"3","key":"433_CR61","doi-asserted-by":"crossref","first-page":"1239","DOI":"10.1152\/japplphysiol.00241.2001","volume":"92","author":"T Heldt","year":"2002","unstructured":"Heldt T, Shim EB, Kamm RD, Mark RG. Computational modeling of cardiovascular response to orthostatic stress. J Appl Physiol. 2002; 92(3):1239\u201354.","journal-title":"J Appl Physiol"},{"issue":"1","key":"433_CR62","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/BF00250853","volume":"66","author":"M Feinberg","year":"1977","unstructured":"Feinberg M, Horn FJ. Chemical mechanism structure and the coincidence of the stoichiometric and kinetic subspaces. Arch Ration Mech Anal. 1977; 66(1):83\u201397.","journal-title":"Arch Ration Mech Anal"},{"key":"433_CR63","unstructured":"Tsatsos M. Theoretical and Numerical study of the Van der Pol equation. PhD thesis, Aristotle University of Thessaloniki. 2006."},{"issue":"06","key":"433_CR64","doi-asserted-by":"crossref","first-page":"1529","DOI":"10.1142\/S0218127493001203","volume":"3","author":"R Mettin","year":"1993","unstructured":"Mettin R, Parlitz U, Lauterborn W. Bifurcation structure of the driven Van der Pol oscillator. Int J Bifurcation Chaos. 1993; 3(06):1529\u201355.","journal-title":"Int J Bifurcation Chaos"},{"issue":"3","key":"433_CR65","doi-asserted-by":"crossref","first-page":"1428","DOI":"10.1103\/PhysRevA.36.1428","volume":"36","author":"U Parlitz","year":"1987","unstructured":"Parlitz U, Lauterborn W. Period-doubling cascades and devil\u2019s staircases of the driven van der Pol oscillator. Phys Rev A. 1987; 36(3):1428.","journal-title":"Phys Rev A"},{"issue":"23","key":"433_CR66","doi-asserted-by":"crossref","first-page":"2230","DOI":"10.1016\/j.physleta.2011.04.037","volume":"375","author":"G Leonov","year":"2011","unstructured":"Leonov G, Kuznetsov N, Vagaitsev V. Localization of hidden Chua\u2019s attractors. Phys Lett A. 2011; 375(23):2230\u20133.","journal-title":"Phys Lett A"},{"issue":"1","key":"433_CR67","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/0167-2789(83)90119-7","volume":"7","author":"L Glass","year":"1983","unstructured":"Glass L, Guevara MR, Shrier A, Perez R. Bifurcation and chaos in a periodically stimulated cardiac oscillator. Phys D Nonlinear Phenom. 1983; 7(1):89\u2013101.","journal-title":"Phys D Nonlinear Phenom"},{"issue":"1","key":"433_CR68","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1137\/140988784","volume":"5","author":"H Du","year":"2017","unstructured":"Du H, Smith LA. Rising Above Chaotic Likelihoods. SIAM\/ASA J Uncertain Quantif. 2017; 5(1):246\u201358.","journal-title":"SIAM\/ASA J Uncertain Quantif"},{"issue":"1","key":"433_CR69","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/0167-2789(93)90006-M","volume":"65","author":"D Poland","year":"1993","unstructured":"Poland D. Cooperative catalysis and chemical chaos: a chemical model for the Lorenz equations. Phys D Nonlinear Phenom. 1993; 65(1):86\u201399.","journal-title":"Phys D Nonlinear Phenom"},{"issue":"1","key":"433_CR70","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pcbi.1005331","volume":"13","author":"F Fr\u00f6hlich","year":"2017","unstructured":"Fr\u00f6hlich F, Kaltenbacher B, Theis FJ, Hasenauer J. Scalable parameter estimation for genome-scale biochemical reaction networks. PLoS Comput Biol. 2017; 13(1):1\u201318.","journal-title":"PLoS Comput Biol"},{"issue":"5","key":"433_CR71","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1007\/s11222-011-9269-5","volume":"22","author":"M Vihola","year":"2012","unstructured":"Vihola M. Robust adaptive metropolis algorithm with coerced acceptance rate. Stat Comput. 2012; 22(5):997\u20131008.","journal-title":"Stat Comput"},{"key":"433_CR72","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1214\/088342305000000016","volume":"20","author":"A Jasra","year":"2005","unstructured":"Jasra A, Holmes CC, Stephens DA. Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling. Stat Sci. 2005; 20:50\u201367.","journal-title":"Stat Sci"},{"issue":"2","key":"433_CR73","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/s11009-011-9238-7","volume":"15","author":"P Papastamoulis","year":"2013","unstructured":"Papastamoulis P, Iliopoulos G. On the convergence rate of random permutation sampler and ECR algorithm in missing data models. Methodol Comput Appl Probab. 2013; 15(2):293\u2013304.","journal-title":"Methodol Comput Appl Probab"},{"key":"433_CR74","doi-asserted-by":"crossref","first-page":"2467","DOI":"10.1101\/gr.1262503","volume":"13","author":"CG Moles","year":"2003","unstructured":"Moles CG, Mendes P, Banga JR. Parameter estimation in biochemical pathways: A comparison of global optimization methods. Genome Res. 2003; 13:2467\u201374.","journal-title":"Genome Res"},{"issue":"15","key":"433_CR75","doi-asserted-by":"crossref","first-page":"2321","DOI":"10.1093\/bioinformatics\/btw131","volume":"32","author":"S Hross","year":"2016","unstructured":"Hross S, Hasenauer J. Analysis of CFSE time-series data using division-, age- and label-structured population models. Bioinformatics. 2016; 32(15):2321\u201329.","journal-title":"Bioinformatics"},{"key":"433_CR76","doi-asserted-by":"crossref","DOI":"10.1201\/9781420011432","volume-title":"An Introduction to Systems Biology: Design Principles of Biological Circuits","author":"U Alon","year":"2006","unstructured":"Alon U. An Introduction to Systems Biology: Design Principles of Biological Circuits. Boca Raton: CRC press; 2006."},{"issue":"1","key":"433_CR77","first-page":"1593","volume":"15","author":"MD Hoffman","year":"2014","unstructured":"Hoffman MD, Gelman A. The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. J Mach Learn Res. 2014; 15(1):1593\u2013623.","journal-title":"J Mach Learn Res"},{"key":"433_CR78","volume-title":"Proceedings of the AAAI Conference on Artificial Intelligence, vol. 2014","author":"S Lan","year":"2014","unstructured":"Lan S, Streets J, Shahbaba B. Wormhole Hamiltonian Monte Carlo. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 2014. Rockville Pike: National Center for Biotechnology Information (NCBI): 2014. p. 1953."},{"issue":"1","key":"433_CR79","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1198\/jcgs.2010.09035","volume":"20","author":"Y Bai","year":"2011","unstructured":"Bai Y, Craiu RV, Di Narzo AF. Divide and conquer: a mixture-based approach to regional adaptation for MCMC. J Comput Graph Stat. 2011; 20(1):63\u201379.","journal-title":"J Comput Graph Stat"},{"key":"433_CR80","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.csda.2016.12.007","volume":"109","author":"M B\u00e9dard","year":"2017","unstructured":"B\u00e9dard M. Hierarchical models: Local proposal variances for RWM-within-Gibbs and MALA-within-Gibbs. Comput Stat Data Anal. 2017; 109:231\u201346.","journal-title":"Comput Stat Data Anal"},{"issue":"5","key":"433_CR81","doi-asserted-by":"crossref","first-page":"04016016","DOI":"10.1061\/(ASCE)EM.1943-7889.0001066","volume":"142","author":"W Betz","year":"2016","unstructured":"Betz W, Papaioannou I, Straub D. Transitional Markov Chain Monte Carlo: Observations and Improvements. J Eng Mech. 2016; 142(5):04016016.","journal-title":"J Eng Mech"},{"issue":"02","key":"433_CR82","doi-asserted-by":"crossref","first-page":"02043","DOI":"10.1088\/1742-5468\/2009\/02\/P02043","volume":"2009","author":"T Yanagita","year":"2009","unstructured":"Yanagita T, Iba Y. Exploration of order in chaos using the replica exchange Monte Carlo method. J Stat Mech Theory Exp. 2009; 2009(02):02043.","journal-title":"J Stat Mech Theory Exp"},{"issue":"3","key":"433_CR83","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1080\/00031305.1992.10475878","volume":"46","author":"G Casella","year":"1992","unstructured":"Casella G, George EI. Explaining the gibbs sampler. Am Stat. 1992; 46(3):167\u201374.","journal-title":"Am Stat"},{"key":"433_CR84","volume-title":"Information Theory, Inference, and Learning Algorithms","author":"DJC MacKay","year":"2005","unstructured":"MacKay DJC. Information Theory, Inference, and Learning Algorithms, 7.2 ed. Cambridge: Cambridge University Press; 2005."},{"key":"433_CR85","volume-title":"Proceedings of the 12th International Conference on Computational Methods in Systems Biology (CMSB 2014)","year":"2014","unstructured":"Fr\u00f6hlich F, Hross S, Theis FJ, Hasenauer J. In: Mendes P, Dada JO, Smallbone KO, (eds).Proceedings of the 12th International Conference on Computational Methods in Systems Biology (CMSB 2014). Manchester: Springer; 2014. pp. 73\u201385."}],"container-title":["BMC Systems Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s12918-017-0433-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,24]],"date-time":"2024-06-24T23:46:36Z","timestamp":1719272796000},"score":1,"resource":{"primary":{"URL":"http:\/\/bmcsystbiol.biomedcentral.com\/articles\/10.1186\/s12918-017-0433-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,24]]},"references-count":85,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["433"],"URL":"https:\/\/doi.org\/10.1186\/s12918-017-0433-1","relation":{},"ISSN":["1752-0509"],"issn-type":[{"value":"1752-0509","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,6,24]]},"article-number":"63"}}