Abstract
In this paper, we introduce NPBayes-fMRI, a user-friendly MATLAB GUI that implements a unified, probabilistically coherent non-parametric Bayesian framework for the analysis of task-related fMRI data from multi-subject experiments. The modeling approach is based on a spatio-temporal linear regression model that specifically accounts for the between-subjects heterogeneity in neuronal activity via a spatially informed multi-subject non-parametric variable selection prior. A characteristic feature of the approach is that it results in a clustering of the subjects into subgroups characterized by similar brain responses, while simultaneously producing group-level as well as subject-level activation maps. This is distinct from two-stage “group analysis” approaches traditionally considered in the fMRI literature, which separate the inference on the individual fMRI time courses from the inference at the population level. Here, we first describe the models and a Variational Bayes algorithm for posterior inference. Next, we introduce the toolbox and illustrate its features via an example.
Similar content being viewed by others
References
Bishop C (2006) Pattern recognition and machine learning. Springer, Berlin
Bowman F, Caffo B, Bassett S, Kilts C (2008) A Bayesian hierarchical framework for spatial modeling of fMRI data. NeuroImage 39(1):146–156
Buxton R, Frank L (1997) A model for the coupling between cerebral blood flow and oxygen metabolism during neural stimulation. J Cereb Blood Flow Metab 17(1):64–72
Cerliani L, Thomas M, Aquino D, Contarino V, Bizzi A (2017) Disentangling subgroups of participants recruiting shared as well as different brain regions for the execution of the verb generation task: a data-driven fMRI data. Cortex 86:247–259
Efron B (2008) Microarrays, empirical Bayes and the two-groups model. Stat Science 23(1):1–22
Fadili M, Bullmore E (2002) Wavelet-generalised least squares: a new BLU estimator of linear regression models with 1/f errors. NeuroImage 15:217–232
Fischer-Baum S, Kook J, Lee Y, Ramos-Nunez A, Vannucci M (2017) Sight or sound? Heterogeneity in the neural and cognitive mechanisms of single word reading (submitted).
Flandin G, Penny W (2007) Bayesian fMRI data analysis with sparse spatial basis function priors. NeuroImage 34(3):1108–1125
Friston K (2011) Functional and effective connectivity: a review. Brain Connect 1(1):13–36
Friston K, Jezzard P, Turner R (1994) Analysis of functional MRI time-series. Human Brain Mapp 1(2):153–171
Friston K, Holmes A, Poline J, Grasby P, Williams S, Frackowiak R, Turner R (1995) Analysis of fMRI time-series revisited. NeuroImage 2(1):45–53
Friston K, Penny W, Phillips C, Kiebel S, Hinton G, Ashburner J (2002) Classical and Bayesian inference in neuroimaging: theory. NeuroImage 16:465–483
Friston KJ (1994) Functional and effective connectivity in neuroimaging: a synthesis. Human Brain Mapp 2:56–78
Harrison L, Green G (2010) A Bayesian spatiotemporal model for very large data sets. NeuroImage 50(3):1126–1141
Holmes A, Friston K (1998) Generalisability, random effects & population inference. NeuroImage 7:S754
Jeong J, Vannucci M, Ko K (2013) A wavelet-based Bayesian approach to regression models with long memory errors and its application to fMRI data. Biometrics 69:184–196
Lee K, Jones G, Caffo B, Bassett S (2014) Spatial Bayesian variable selection models on functional magnetic resonance imaging time-series data. Bayesian Anal 9(3):699–732
Li F, Zhang T, Wang Q, MZ G, EL M, Coan J (2015) Spatial Bayesian variable selection and grouping in high-dimensional scalar-on-image regressions. Ann Appl Stat 9(2):687–713
Lindquist M (2008) The statistical analysis of fMRI data. Stat Sci 23(4):439–464
Meyer F (2003) Wavelet-based estimation of a semiparametric generalized linear model of fMRI time-series. IEEE Trans Med Imaging 22(3):315–322
Newton M, Noueiry A, Sarkar D, Ahlquist P (2004) Detecting differential gene expression with a semiparametric hierarchical mixture method. Biostatistics 5(2):155–176
Penny W, Kiebel S, Friston K (2003) Variational bayesian inference for fmri time series. NeuroImage 19(3):727–741
Penny W, Trujillo-Barreto N, Friston K (2005) Bayesian fMRI time series analysis with spatial priors. NeuroImage 24(2):350–362
Propp J, Wilson D (1996) Exact sampling with coupled markov chains and applications to statistical mechanics. Random Struct Algorithms 9(1):223–252
Quirós A, Diez R, Gamerman D (2010) Bayesian spatiotemporal model of fMRI data. NeuroImage 49(1):442–456
Rue H, Maritno S, Chopin N (2009) Approximate Bayesian inference for latent Gaussian models by using integrate nested Laplace approximations. J Royal Stat Soc Ser B 71:319–392
Sanyal N, Ferreira M (2012) Bayesian hierarchical multi-subject multiscale analysis of functional MRI data. NeuroImage 63(3):1519–1531
Smith M, Fahrmeir L (2007) Spatial Bayesian variable selection with application to functional magnetic resonance imaging. J Am Stat Assoc 102(478):417–431
Su S, Caffo B, Garrett-Mayer E, Bassett S (2009) Modified test statistics by inter-voxel variance shrinkage with an application to fMRI. Biostatistics 10(2):219–227
Sun W, Reich B, Cai T, Guindani M, Schwartzman A (2015) False discovery control in large-scale spatial multiple testing. J Royal Stat Soc 77(1):59–83
Teh Y, Jordan M, Beal M, Blei D (2006) Hierarchical Dirichlet processes. J Am Stat Assoc 101(476):1–8
Wang C, Paisley J, Blei D (2011) Online variational inference for the hierarchical Dirichlet process. International Conference on Artificial Intelligence and Statistics pp 752–760
Woolrich M, Jenkinson M, Brady J, Smith S (2004) Fully Bayesian spatio-temporal modeling of fMRI data. IEEE Trans Med Imaging 23(2):213–231
Woolrich M, Behrens T, Smith S (2004b) Constrained linear basis sets for HRF modelling using variational Bayes. NeuroImage 21(4):1748–1761
Wornell G, Oppenheim A (1992) Estimation of fractal signals from noisy measurements using wavelets. IEEE Trans Signal Process 40(3):611–623
Worsley K, Friston K (1995) Analysis of fMRI time-series revisited-again. NeuroImage 2:173–181
Xia J, Liang F, Wang Y (2009) fMRI analysis through Bayesian variable selection with a spatial prior. IEEE International Symposium on Biomedical Imaging pp 714–717
Zhang L, Guindani M, Versace F, Vannucci M (2014) A spatio-temporal nonparametric Bayesian variable selection model of fMRI data for clustering correlated time courses. NeuroImage 95:162–175
Zhang L, Guindani M, Vannucci M (2015) Bayesian models for fMRI data analysis. WIREs Comput Stat 7(1):21–41
Zhang L, Guindani M, Versace F, Englemann J, Vannucci M (2016) A spatiotemporal nonparametric Bayesian model of multi-subject fMRI data. Ann Appl Stat 10(2):638–666
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was partially supported by NSF-SES 1659921 and NSF-SES-1659925.
Rights and permissions
About this article
Cite this article
Kook, J.H., Guindani, M., Zhang, L. et al. NPBayes-fMRI: Non-parametric Bayesian General Linear Models for Single- and Multi-Subject fMRI Data. Stat Biosci 11, 3–21 (2019). https://doi.org/10.1007/s12561-017-9205-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12561-017-9205-0