A spatiotemporal nonparametric Bayesian model of multi-subject fMRI data. (English) Zbl 1400.62299

Summary: In this paper we propose a unified, probabilistically coherent framework for the analysis of task-related brain activity in multi-subject fMRI experiments. 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. In our modeling approach we consider a spatiotemporal linear regression model and specifically account for the between-subjects heterogeneity in neuronal activity via a spatially informed multi-subject nonparametric variable selection prior. For posterior inference, in addition to Markov chain Monte Carlo sampling algorithms, we develop suitable variational Bayes algorithms. We show on simulated data that variational Bayes inference achieves satisfactory results at more reduced computational costs than using MCMC, allowing scalability of our methods. In an application to data collected to assess brain responses to emotional stimuli our method correctly detects activation in visual areas when visual stimuli are presented.


62P10 Applications of statistics to biology and medical sciences; meta analysis
62M30 Inference from spatial processes
62G08 Nonparametric regression and quantile regression
62F15 Bayesian inference
92C55 Biomedical imaging and signal processing


spBayes; PRMLT
Full Text: DOI Euclid


[1] Banerjee, S., Carlin, B. P. and Gelfand, A. E. (2015). Hierarchical Modeling and Analysis for Spatial Data , 2nd ed. Monographs on Statistics and Applied Probability 135 . CRC Press, Boca Raton, FL. · Zbl 1358.62009
[2] Barrientos, A. F., Jara, A. and Quintana, F. A. (2012). On the support of MacEachern’s dependent Dirichlet processes and extensions. Bayesian Anal. 7 277-309. · Zbl 1330.60067 · doi:10.1214/12-BA709
[3] Bishop, C. M. (2006). Pattern Recognition and Machine Learning . Springer, New York. · Zbl 1107.68072
[4] Blei, D. M. and Jordan, M. I. (2006). Variational inference for Dirichlet process mixtures. Bayesian Anal. 1 121-143 (electronic). · Zbl 1331.62259 · doi:10.1214/06-BA104
[5] Bowman, F., Caffo, B., Bassett, S. and Kilts, C. (2008). A Bayesian hierarchical framework for spatial modeling of fMRI data. NeuroImage 39 146-156.
[6] Buxton, R. and Frank, L. (1997). A model for the coupling between cerebral blood flow and oxygen metabolism during neural stimulation. J. Cereb. Blood Flow Metab. 17 64-72.
[7] Carbonetto, P. and Stephens, M. (2012). Scalable variational inference for Bayesian variable selection in regression, and its accuracy in genetic association studies. Bayesian Anal. 7 73-107. · Zbl 1330.62089 · doi:10.1214/12-BA703
[8] Daubechies, I. (1992). Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics 61 . SIAM, Philadelphia, PA. · Zbl 0776.42018
[9] Efron, B. (2008). Microarrays, empirical Bayes and the two-groups model. Statist. Sci. 23 1-22. · Zbl 1327.62046 · doi:10.1214/07-STS236
[10] Fadili, M. J. and Bullmore, E. T. (2002). Wavelet-generalised least squares: A new BLU estimator of linear regression models with \(1/f\) errors. NeuroImage 15 217-232.
[11] Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1 209-230. · Zbl 0255.62037 · doi:10.1214/aos/1176342360
[12] Flandin, G. and Penny, W. D. (2007). Bayesian fMRI data analysis with sparse spatial basis function priors. NeuroImage 34 1108-1125.
[13] Friston, K. J. (1994). Functional and effective connectivity in neuroimaging: A synthesis. Hum. Brain Mapp. 2 56-78.
[14] Friston, K. J. (2011). Functional and effective connectivity: A review. Brain Connectivity 1 13-36.
[15] Friston, K. J., Jezzard, P. and Turner, R. (1994). Analysis of functional MRI time-series. Hum. Brain Mapp. 1 153-171.
[16] Friston, K. J. and Penny, W. (2003). Posterior probability maps and SPMs. NeuroImage 19 1240-1249.
[17] Friston, K. J., Holmes, A. P., Poline, J. B., Grasby, P. J., Williams, S. C. R., Frackowiak, R. S. J. and Turner, R. (1995). Analysis of fMRI time-series revisited. NeuroImage 2 45-53.
[18] Friston, K. J., Penny, W., Phillips, C., Kiebel, S., Hinton, G. and Ashburner, J. (2002). Classical and Bayesian inference in neuroimaging: Theory. NeuroImage 16 465-483.
[19] Harrison, L. M. and Green, G. G. R. (2010). A Bayesian spatiotemporal model for very large data sets. NeuroImage 50 1126-1141.
[20] Hartvig, N. V. and Jensen, J. L. (2000). Spatial mixture modeling of fMRI data. Hum. Brain Mapp. 11 233-248.
[21] Holmes, A. P. and Friston, K. J. (1998). Generalisability, random effects & population inference. Neuroimage 7 S754.
[22] Ishwaran, H. and James, L. F. (2001). Gibbs sampling methods for stick-breaking priors. J. Amer. Statist. Assoc. 96 161-173. · Zbl 1014.62006 · doi:10.1198/016214501750332758
[23] Jbabdi, S., Woolrich, M. W. and Behrens, T. E. J. (2009). Multiple-subjects connectivity-based parcellation using hierarchical Dirichlet process mixture models. NeuroImage 44 373-384.
[24] Jeong, J., Vannucci, M. and 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. · Zbl 1270.62057 · doi:10.1111/j.1541-0420.2012.01819.x
[25] Johnson, T. D., Liu, Z., Bartsch, A. J. and Nichols, T. E. (2013). A Bayesian non-parametric Potts model with application to pre-surgical FMRI data. Stat. Methods Med. Res. 22 364-381. · doi:10.1177/0962280212448970
[26] Joset, A. E., Gazzola, V. and Keysers, C. (2009). An introduction to anatomical ROI-based fMRI classification analysis. Brain Res. 1282 114-125.
[27] Kalus, S., Sämann, P. G. and Fahrmeir, L. (2014). Classification of brain activation via spatial Bayesian variable selection in fMRI regression. Adv. Data Anal. Classif. 8 63-83. · doi:10.1007/s11634-013-0142-6
[28] Kim, S., Smyth, P. and Stern, H. (2006). A nonparametric Bayesian approach to detecting spatial activation patterns in fMRI data. In Medical Image Computing and Computer-Assisted Intervention-MICCAI 2006 217-224.
[29] Lee, K.-J., Jones, G. L., Caffo, B. S. and Bassett, S. S. (2014). Spatial Bayesian variable selection models on functional magnetic resonance imaging time-series data. Bayesian Anal. 9 699-731. · Zbl 1327.62507 · doi:10.1214/14-BA873
[30] Li, F., Zhang, T., Wang, Q., Gonzalez, M. Z., Maresh, E. L. and Coan, J. A. (2015). Spatial Bayesian variable selection and grouping for high-dimensional scalar-on-image regression. Ann. Appl. Stat. 9 687-713. · Zbl 1397.62458 · doi:10.1214/15-AOAS818
[31] Lindquist, M. A. (2008). The statistical analysis of fMRI data. Statist. Sci. 23 439-464. · Zbl 1329.62296 · doi:10.1214/09-STS282
[32] Meyer, F. G. (2003). Wavelet-based estimation of a semiparametric generalized linear model of fMRI time-series. IEEE Trans. Med. Imag. 22 315-322.
[33] Müller, P., Parmigiani, G. and Rice, K. (2007). FDR and Bayesian multiple comparisons rules. In Bayesian Statistics 8 (J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West, eds.). Oxford Sci. Publ. 349-370. Oxford Univ. Press, Oxford. · Zbl 1252.62025
[34] Newton, M. A., Noueiry, A., Sarkar, D. and Ahlquist, P. (2004). Detecting differential gene expression with a semiparametric hierarchical mixture method. Biostatistics 5 155-176. · Zbl 1096.62124 · doi:10.1093/biostatistics/5.2.155
[35] Penny, W., Kiebel, S. and Friston, K. J. (2003). Variational Bayesian inference for fmri time series. NeuroImage 19 727-741.
[36] Penny, W. D., Trujillo-Barreto, N. and Friston, K. J. (2005). Bayesian fMRI time series analysis with spatial priors. NeuroImage 24 350-362.
[37] Propp, J. G. and Wilson, D. B. (1996). Exact sampling with coupled Markov chains and applications to statistical mechanics. In Proceedings of the Seventh International Conference on Random Structures and Algorithms ( Atlanta , GA , 1995) 9 223-252. Random Structures Algorithms, 1-2. · Zbl 0859.60067 · doi:10.1002/(SICI)1098-2418(199608/09)9:1/2<223::AID-RSA14>3.0.CO;2-O
[38] Quirós, A., Diez, R. M. and Gamerman, D. (2010). Bayesian spatiotemporal model of fMRI data. NeuroImage 49 442-456.
[39] Raftery, A. E. and Lewis, S. M. (1992). One long run with diagnostics: Implementation strategies for Markov chain Monte Carlo. Statist. Sci. 7 493-497.
[40] Rodríguez, A., Dunson, D. B. and Gelfand, A. E. (2008). The nested Dirichlet process. J. Amer. Statist. Assoc. 103 1131-1144. · Zbl 1205.62062 · doi:10.1198/016214508000000553
[41] Rosenblatt, J. D., Vink, M. and Benjamini, Y. (2014). Revisiting multi-subject random effects in fMRI: Advocating prevalence estimation. NeuroImage 84 113-121.
[42] Rue, H., Martino, S. and Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J. R. Stat. Soc. Ser. B Stat. Methodol. 71 319-392. · Zbl 1248.62156 · doi:10.1111/j.1467-9868.2008.00700.x
[43] Sanyal, N. and Ferreira, M. A. (2012). Bayesian hierarchical multi-subject multiscale analysis of functional MRI data. NeuroImage 63 1519-1531.
[44] Savitsky, T. and Vannucci, M. (2010). Spiked Dirichlet process priors for Gaussian process models. J. Probab. Stat. Art. ID 201489, 14. · Zbl 1214.62100 · doi:10.1155/2010/201489
[45] Savitsky, T., Vannucci, M. and Sha, N. (2011). Variable selection for nonparametric Gaussian process priors: Models and computational strategies. Statist. Sci. 26 130-149. · Zbl 1222.65017 · doi:10.1214/11-STS354
[46] Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statist. Sinica 4 639-650. · Zbl 0823.62007
[47] Smith, M. and Fahrmeir, L. (2007). Spatial Bayesian variable selection with application to functional magnetic resonance imaging. J. Amer. Statist. Assoc. 102 417-431. · Zbl 1134.62322 · doi:10.1198/016214506000001031
[48] Su, S., Caffo, B., Garrett-Mayer, E. and Bassett, S. (2009). Modified test statistics by inter-voxel variance shrinkage with an application to fMRI. Biostatistics 10 219-227.
[49] Sun, W., Reich, B. J., Cai, T. T., Guindani, M. and Schwartzman, A. (2015). False discovery control in large-scale spatial multiple testing. J. R. Stat. Soc. Ser. B. Stat. Methodol. 77 59-83. · doi:10.1111/rssb.12064
[50] Teh, Y. W., Jordan, M. I., Beal, M. J. and Blei, D. M. (2006). Hierarchical Dirichlet processes. J. Amer. Statist. Assoc. 101 1566-1581. · Zbl 1171.62349 · doi:10.1198/016214506000000302
[51] Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., Mazoyer, B. and Joliot, M. (2002). Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. NeuroImage 15 273-289.
[52] Versace, F., Engelmann, J. M., Jackson, E. F., Slapin, A., Cortese, K. M., Bevers, T. B. and Schover, L. R. (2013). Brain responses to erotic and other emotional stimuli in breast cancer survivors with and without distress about low sexual desire: A preliminary fmri study. Brain Imaging Behav. 7 533-542.
[53] Wang, C., Paisley, J. W. and Blei, D. M. (2011). Online variational inference for the hierarchical Dirichlet process. In International Conference on Artificial Intelligence and Statistics 752-760.
[54] Woolrich, M. W., Behrens, T. and Smith, S. (2004). Constrained linear basis sets for HRF modelling using variational Bayes. NeuroImage 21 1748-1761.
[55] Woolrich, M. W., Jenkinson, M., Brady, J. M. and Smith, S. M. (2004). Fully Bayesian spatio-temporal modeling of fMRI data. IEEE Trans. Med. Imag. 23 213-231.
[56] Wornell, G. W. and Oppenheim, A. V. (1992). Estimation of fractal signals from noisy measurements using wavelets. IEEE Trans. Signal Process. 40 611-623.
[57] Worsley, K. J. and Friston, K. J. (1995). Analysis of fMRI time-series revisited-again. NeuroImage 2 173-181.
[58] Xia, J., Liang, F. and Wang, Y. (2009). FMRI analysis through Bayesian variable selection with a spatial prior. IEEE Int. Symp. on Biomedical Imaging 714-717.
[59] Xu, L., Johnson, T. D., Nichols, T. E. and Nee, D. E. (2009). Modeling inter-subject variability in fMRI activation location: A Bayesian hierarchical spatial model. Biometrics 65 1041-1051. · Zbl 1181.62099 · doi:10.1111/j.1541-0420.2008.01190.x
[60] Yan, F., Xu, N. and Qi, Y. (2009). Parallel inference for latent dirichlet allocation on graphics processing units. In Advances in Neural Information Processing Systems 2134-2142.
[61] Zhang, L., Guindani, M., Versace, F. and Vannucci, M. (2014). A spatio-temporal nonparametric Bayesian variable selection model of fMRI data for clustering correlated time courses. NeuroImage 95 162-175.
[62] Zhang, L., Guindani, M. and Vannucci, M. (2015). Bayesian models for fMRI data analysis. Wiley Interdiscip. Rev. : Comput. Stat. 7 21-41. · doi:10.1002/wics.1339
[63] Zhang, L., Guindani, M., Versace, F., Engelmann, J. and Vannucci, M. (2016). Supplement to “A spatiotemporal nonparametric Bayesian model of multi-subject fMRI data.” . · Zbl 1400.62299 · doi:10.1214/16-AOAS926
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.