{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T20:54:29Z","timestamp":1762376069677},"reference-count":60,"publisher":"Public Library of Science (PLoS)","issue":"3","license":[{"start":{"date-parts":[[2016,3,4]],"date-time":"2016-03-04T00:00:00Z","timestamp":1457049600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"DOI":"10.1371\/journal.pcbi.1004797","type":"journal-article","created":{"date-parts":[[2016,3,4]],"date-time":"2016-03-04T13:38:42Z","timestamp":1457098722000},"page":"e1004797","update-policy":"http:\/\/dx.doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":11,"title":["Annealed Importance Sampling for Neural Mass Models"],"prefix":"10.1371","volume":"12","author":[{"given":"Will","family":"Penny","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Biswa","family":"Sengupta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2016,3,4]]},"reference":[{"key":"ref1","article-title":"Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems","author":"P Dayan","year":"2001"},{"issue":"8","key":"ref2","doi-asserted-by":"crossref","first-page":"e1000092","DOI":"10.1371\/journal.pcbi.1000092","article-title":"The dynamic brain: from spiking neurons to neural masses and cortical fields","volume":"4","author":"G Deco","year":"2008","journal-title":"PLoS Comput Biol"},{"issue":"4","key":"ref3","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1016\/S1053-8119(03)00202-7","article-title":"Dynamic Causal Modelling","volume":"19","author":"K Friston","year":"2003","journal-title":"Neuroimage"},{"issue":"2","key":"ref4","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1016\/j.neuroimage.2009.04.062","article-title":"Dynamic causal modelling of distributed electromagnetic responses","volume":"47","author":"J Daunizeau","year":"2009","journal-title":"Neuroimage"},{"issue":"8","key":"ref5","doi-asserted-by":"crossref","first-page":"e22790","DOI":"10.1371\/journal.pone.0022790","article-title":"Dynamic causal models and physiological inference: a validation study using isoflurane anaesthesia in rodents","volume":"6","author":"R Moran","year":"2011","journal-title":"PLoS One"},{"issue":"1","key":"ref6","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.neuroimage.2006.08.035","article-title":"Variational free energy and the Laplace approximation","volume":"34","author":"K Friston","year":"2007","journal-title":"Neuroimage"},{"key":"ref7","article-title":"Pattern Recognition and Machine Learning","author":"CM Bishop","year":"2006"},{"key":"ref8","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1080\/01621459.1986.10478240","article-title":"Accurate Approximations for Posterior Moments and Marginal Densities","volume":"81","author":"L Tierney","year":"1986","journal-title":"Journal of the American Statistical Association"},{"key":"ref9","article-title":"On the asymptotic behaviour of posterior distributions","volume":"31","author":"A Walker","year":"1969","journal-title":"Journal of the Royal Statistical Society"},{"key":"ref10","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1016\/j.neuroimage.2009.11.062","article-title":"Dynamic causal modelling: A critical review of the biophysical and statistical foundations","volume":"58","author":"J Daunizeau","year":"2011","journal-title":"Neuroimage"},{"key":"ref11","doi-asserted-by":"crossref","DOI":"10.1007\/b98874","article-title":"Numerical Optimization","author":"J Nocedal","year":"1999"},{"issue":"12","key":"ref12","doi-asserted-by":"crossref","first-page":"3052","DOI":"10.1162\/neco.2006.18.12.3052","article-title":"Bifurcation analysis of Jansen\u2019s neural mass model","volume":"18","author":"F Grimbert","year":"2006","journal-title":"Neural Comput"},{"key":"ref13","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1023\/A:1008923215028","article-title":"Annealed Importance Sampling","volume":"11","author":"RM Neal","year":"2001","journal-title":"Statistics and Computing"},{"issue":"2","key":"ref14","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1111\/j.1467-9868.2010.00765.x","article-title":"Riemann manifold Langevin and Hamiltonian Monte Carlo methods","volume":"73","author":"M Girolami","year":"2011","journal-title":"Journal of the Royal Statistical Society Series B"},{"key":"ref15","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1016\/j.neuroimage.2015.07.043","article-title":"Gradient-based MCMC samplers for Dynamic Causal Modelling","volume":"125","author":"B Sengupta","journal-title":"Neuroimage"},{"issue":"3","key":"ref16","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1016\/j.neuroimage.2007.07.028","article-title":"A Metropolis-Hastings algorithm for dynamic causal models","volume":"38","author":"J Chumbley","year":"2007","journal-title":"Neuroimage"},{"issue":"4","key":"ref17","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1016\/j.neuroimage.2005.10.045","article-title":"Dynamic causal modeling of evoked responses in EEG and MEG","volume":"30","author":"O David","year":"2006","journal-title":"Neuroimage"},{"key":"ref18","doi-asserted-by":"crossref","DOI":"10.1201\/9780429258411","article-title":"Bayesian Data Analysis","author":"A Gelman","year":"1995"},{"key":"ref19","article-title":"Handbook of Markov Chain Monte Carlo","author":"R Neal","year":"2011"},{"key":"ref20","article-title":"Designing and building parallel programs","author":"I Foster","year":"1995"},{"issue":"12","key":"ref21","doi-asserted-by":"crossref","first-page":"4028","DOI":"10.1016\/j.csda.2009.07.025","article-title":"Estimating Bayes factors via thermodynamic integration and population MCMC","volume":"53","author":"B Calderhead","year":"2009","journal-title":"Computational Statistics & Data Analysis"},{"issue":"3","key":"ref22","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1111\/j.1467-9868.2007.00650.x","article-title":"Marginal likelihood estimation via power posteriors","volume":"70","author":"N Friel","year":"2008","journal-title":"Journal of the Royal Statistical Society: Series B"},{"key":"ref23","article-title":"Gatsby Computational Neuroscience Unit","author":"M Beal","year":"2003"},{"issue":"6","key":"ref24","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1093\/bioinformatics\/btm607","article-title":"Bayesian ranking of biochemical system models","volume":"24","author":"V Vyshemirsky","year":"2008","journal-title":"Bioinformatics"},{"issue":"2","key":"ref25","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1214\/ss\/1028905934","article-title":"Simulating Normalizing Constants: From Importance Sampling to Bridge Sampling to Path Sampling","volume":"13","author":"A Gelman","year":"1998","journal-title":"Statistical Science"},{"key":"ref26","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-4541-9","article-title":"An introduction to the bootstrap","author":"B Efron","year":"1993"},{"key":"ref27","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1098\/rsfs.2011.0051","article-title":"Statistical analysis of nonlinear dynamical systems using differential geometric sampling methods","volume":"1","author":"B Calderhead","year":"2011","journal-title":"Interface Focus"},{"key":"ref28","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/j.neuroimage.2014.04.040","article-title":"Efficient Gradient Computation for Dynamical Models","volume":"98","author":"B Sengupta","year":"2014","journal-title":"Neuroimage"},{"key":"ref29","article-title":"Numerical Recipes in C","author":"WH Press","year":"1992"},{"key":"ref30","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316757","article-title":"Nonlinear Regression Analysis and its Applications","author":"D Bates","year":"1988"},{"issue":"439","key":"ref31","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1080\/01621459.1997.10474045","article-title":"Computing Bayes Factors by Combining Simulation and Asymptotic Approximations","volume":"92","author":"T DiCiccio","year":"1997","journal-title":"Journal of the American Statistical Association"},{"key":"ref32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/cercor\/1.1.1","article-title":"Distributed hierarchical processing in the primate cerebral cortex","volume":"1","author":"DJ Felleman","year":"1991","journal-title":"Cerebral Cortex"},{"key":"ref33","doi-asserted-by":"crossref","first-page":"852961","DOI":"10.1155\/2011\/852961","article-title":"EEG and MEG data analysis in SPM8","volume":"2011","author":"V Litvak","year":"2011","journal-title":"Comput Intell Neurosci"},{"key":"ref34","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/BF01891203","article-title":"Approximating the Shapiro-Wilk W-Test for non-normality","volume":"2","author":"J Royston","year":"1992","journal-title":"Statistics and Computing"},{"key":"ref35","article-title":"Roystest:Royston\u2019s Multivariate Normality Test","author":"A Trujillo-Ortiz","year":"2007","journal-title":"A MATLAB file"},{"key":"ref36","article-title":"Practical Markov Chain Monte Carlo","volume":"7","author":"C Geyer","year":"1992","journal-title":"Statistical Science"},{"issue":"1","key":"ref37","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.neuroimage.2011.07.039","article-title":"Comparing Dynamic Causal Models using AIC, BIC and Free Energy","volume":"59","author":"WD Penny","year":"2011","journal-title":"Neuroimage"},{"key":"ref38","first-page":"1","article-title":"Towards automatic model comparison: an adaptive sequential Monte Carlo approach","author":"Y Zhou","year":"2013","journal-title":"ArCHIve"},{"key":"ref39","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.neuroimage.2015.03.008","article-title":"Gradient-free MCMC methods for Dynamic Causal Modelling","volume":"112","author":"B Sengupta","journal-title":"Neuroimage"},{"key":"ref40","article-title":"User Documentation for CVODES, and ODE Solver with Sensitivity Analysis Capabilities","author":"A Hindmarsh","year":"2002"},{"key":"ref41","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.neuroimage.2015.05.084","article-title":"Inversion of Hierarchical Bayesian models using Gaussian processes","volume":"118","author":"E Lomakina","year":"2015","journal-title":"Neuroimage"},{"key":"ref42","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s11222-008-9110-y","article-title":"A tutorial on adaptive MCMC","volume":"18","author":"C Andrieu","year":"2008","journal-title":"Statistics and Computing"},{"issue":"453","key":"ref43","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1198\/016214501750332848","article-title":"Marginal Likelihood from the Metropolis-Hastings Output","volume":"96","author":"S Chib","year":"2001","journal-title":"Journal of the American Statistical Association"},{"issue":"2","key":"ref44","doi-asserted-by":"crossref","first-page":"223","DOI":"10.2307\/3318737","article-title":"An adaptive Metropolis Algorithm","volume":"7","author":"H Haario","year":"2001","journal-title":"Bernoulli"},{"key":"ref45","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1080\/01621459.1995.10476572","article-title":"Bayes factors","volume":"90","author":"RE Kass","year":"1995","journal-title":"Journal of the American Statistical Association"},{"issue":"2","key":"ref46","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1080\/10635150500433722","article-title":"Computing Bayes factors using thermodynamic integration","volume":"55","author":"N Lartillot","year":"2006","journal-title":"Systematic Biology"},{"key":"ref47","article-title":"Thermodynamic Monte Carlo","author":"M Betancourt","year":"2015"},{"key":"ref48","unstructured":"Ma J, Peng J, Wang S, Xu J. Estimating the partition function of graphical models using Langevin Importance Sampling. In: 16th International Conference on Artifical Intelligence and Statistics (AISTATS); 2013."},{"issue":"6","key":"ref49","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0066599","article-title":"Accelerating computation of DCM for ERP in MATLAB by external function calls to the GPU","volume":"8","author":"W Wang","year":"2013","journal-title":"PLoS ONE"},{"key":"ref50","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.jneumeth.2015.09.009","article-title":"MPDCM: A toolbox for massively parallel dynamic causal modelling","volume":"257","author":"E Aponte","journal-title":"Journal of Neuroscience Methods"},{"issue":"49","key":"ref51","doi-asserted-by":"crossref","first-page":"17408","DOI":"10.1073\/pnas.1408184111","article-title":"A general construction for parallelizing Metropolis-Hastings algorithms","volume":"111","author":"B Calderhead","year":"2014","journal-title":"Proceedings of the National Academcy of Sciences"},{"issue":"4","key":"ref52","doi-asserted-by":"crossref","first-page":"041902","DOI":"10.1103\/PhysRevE.71.041902","article-title":"Modeling the effects of anesthesia on the electroencephalogram","volume":"71","author":"I Bojak","year":"2005","journal-title":"Phys Rev E"},{"key":"ref53","article-title":"Stochastic non-linear oscillator models of EEG: the Alzheimer\u2019s disease case","volume":"9","author":"SR P Ghorbanian","year":"2015","journal-title":"Frontiers in Computational Neuroscience"},{"key":"ref54","article-title":"Estimating biophysical parameters from BOLD signals through evolutionary-based optimization","volume":"2015","author":"P Mesejo","journal-title":"Medical Image Computing and Computer-Assisted Intervention (MICCAI)"},{"issue":"52","key":"ref55","doi-asserted-by":"crossref","first-page":"20961","DOI":"10.1073\/pnas.0706274105","article-title":"Evoked brain responses are generated by feedback loops","volume":"104","author":"M Garrido","year":"2007","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"6031","key":"ref56","doi-asserted-by":"crossref","first-page":"858","DOI":"10.1126\/science.1202043","article-title":"Preserved feedforward but impaired top-down processes in the vegetative state","volume":"332","author":"M Boly","year":"2011","journal-title":"Science"},{"issue":"12","key":"ref57","doi-asserted-by":"crossref","first-page":"4260","DOI":"10.1523\/JNEUROSCI.4670-11.2012","article-title":"Changes in Auditory Feedback Connections Determine the Severity of Speech Processing Deficits after Stroke","volume":"32","author":"T Schofield","year":"2012","journal-title":"J Neurosci"},{"key":"ref58","doi-asserted-by":"crossref","DOI":"10.1080\/10618600.2013.805651","article-title":"Annealed Importance Sampling Reversible Jump MCMC Algorithms","volume":"22","author":"G Karagiannis","year":"2013","journal-title":"Journal of Computational and Graphical Statistics"},{"issue":"4","key":"ref59","doi-asserted-by":"crossref","first-page":"2089","DOI":"10.1016\/j.neuroimage.2011.03.062","article-title":"Post-hoc Bayesian model selection","volume":"56","author":"K Friston","year":"2011","journal-title":"Neuroimage"},{"key":"ref60","unstructured":"Salimans T, Welling M. Markov Chain Monte Carlo and Variational Inference: Bridging the Gap. In: International Confernece on Machine Learning; 2014."}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/dx.plos.org\/10.1371\/journal.pcbi.1004797","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,5]],"date-time":"2019-09-05T03:18:16Z","timestamp":1567653496000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1004797"}},"subtitle":[],"editor":[{"given":"Jean","family":"Daunizeau","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2016,3,4]]},"references-count":60,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,3,4]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1004797","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3,4]]}}}