Empirical bayes for DCM: A group inversion scheme

Frontiers in Systems Neuroscience

Volumn 9, Issue November, 2015, Pages

  Friston, Karl ^a   Zeidman, Peter ^a   Litvak, Vladimir ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

Bayesian model reduction; Dynamic causal modeling; Empirical Bayes; Fixed effects; Hierarchical modeling; Random effects

Indexed keywords

CAUSAL MODELING; HUMAN; MOTIVATION; REPRODUCIBILITY;

EID: 84948763031     PISSN: 16625137     EISSN: None     Source Type: Journal    
DOI: 10.3389/fnsys.2015.00164     Document Type: Article

References (15)

1. Efron, B. and Morris, C. (1973). Stein’s estimation rule and its competitors - an empirical Bayes approach. J. Am. Stat. Assoc. 68, 117-130.
2. Fogelson, N., Litvak, V., Peled, A., Fernandez-del-Olmo, M., and Friston, K. (2014). The functional anatomy of schizophrenia: a dynamic causal modeling study of predictive coding. Schizophr. Res. 158, 204-212. doi: 10.1016/j.schres.2014.06.011
3. Friston, K. (2008). Hierarchical models in the brain. PLoS Comput. Biol. 4:e1000211. doi: 10.1371/journal.pcbi.1000211
4. Friston, K. J., Holmes, A. P., Price, C. J., Büchel, C., and Worsley, K. J. (1999). Multisubject fMRI studies and conjunction analyses. Neuroimage 10, 385-396. doi: 10.1006/nimg.1999.0484
5. Friston, K. J., Litvak, V., Oswal, A., Razi, A., Stephan, K. E., van Wijk, B. C., et al. (2015). Bayesian model reduction and empirical Bayes for group (DCM) studies. Neuroimage. doi: 10.1016/j.neuroimage.2015.11.015. [Epub ahead of print]
6. Friston, K., and Penny, W. (2011). Post hoc bayesian model selection. Neuroimage 56, 2089-2099. doi: 10.1016/j.neuroimage.2011.03.062
7. Garrido, M. I., Kilner, J. M., Kiebel, S. J., and Friston, K. J. (2007). Evoked brain responses are generated by feedback loops. Proc. Natl. Acad. Sci. U.S.A. 104, 20961-20966. doi: 10.1073/pnas.0706274105
8. Garrido, M. I., Kilner, J. M., Kiebel, S. J., and Friston, K. J. (2009a). Dynamic causal modeling of the response to frequency deviants. J. Neurophysiol. 101, 2620-2631. doi: 10.1152/jn.90291.2008
9. Garrido, M. I., Kilner, J. M., Kiebel, S. J., Stephan, K. E., Baldeweg, T., and Friston, K. J. (2009b). Repetition suppression and plasticity in the human brain. Neuroimage 48, 269-279. doi: 10.1016/j.neuroimage.2009.06.034
10. Jaakkola, T., and Jordan, M. (1998). "Improving the mean field approximation via the use of mixture distributions," in Learning in Graphical Models, ed M. Jordan (Netherlands: Springer), 163-173.
11. Kass, R. E., and Steffey, D. (1989). Approximate Bayesian inference in conditionally independent hierarchical models (parametric empirical Bayes models). J. Am. Stat. Assoc. 407, 717-726. doi: 10.1080/01621459.1989.10478825
12. Roweis, S., and Ghahramani, Z. (1999). A unifying review of linear Gaussian models. Neural Comput. 11, 305-345. doi: 10.1162/089976699300016674
13. Sengupta, B., Friston, K. J., and Penny, W. D. (2014). Efficient gradient computation for dynamical models. Neuroimage 98, 521-527. doi: 10.1016/j.neuroimage.2014.04.040
14. Woolrich, M. W., Behrens, T. E., Beckmann, C. F., Jenkinson, M., and Smith, S. M. (2004). Multilevel linear modelling for FMRI group analysis using Bayesian inference. Neuroimage 21, 1732-1747. doi: 10.1016/j.neuroimage.2003.12.023
15. Woolrich, M. W., Jbabdi, S., Patenaude, B., Chappell, M., Makni, S., Behrens, T., et al. (2009). Bayesian analysis of neuroimaging data in FSL. Neuroimage 45(Suppl. 1), S173-S186. doi: 10.1016/j.neuroimage.2008.10.055