START UP RESEARCH 2017: Studies in Neural Data Science pp 111-130 | Cite as

Hierarchical Spatio-Temporal Modeling of Resting State fMRI Data

  • Alessia Caponera
  • Francesco Denti
  • Tommaso RigonEmail author
  • Andrea Sottosanti
  • Alan Gelfand
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 257)


In recent years, state of the art brain imaging techniques like Functional Magnetic Resonance Imaging (fMRI), have raised new challenges to the statistical community, which is asked to provide new frameworks for modeling and data analysis. Here, motivated by resting state fMRI data, which can be seen as a collection of spatially dependent functional observations among brain regions, we propose a parsimonious but flexible representation of their dependence structure leveraging a Bayesian time-dependent latent factor model. Adopting an assumption of separability of the covariance structure in space and time, we are able to substantially reduce the computational cost and, at the same time, provide interpretable results. Theoretical properties of the model along with identifiability conditions are discussed. For model fitting, we propose a mcmc algorithm to enable posterior inference. We illustrate our work through an application to a dataset coming from the enkirs project, discussing the estimated covariance structure and also performing model selection along with network analysis. Our modeling is preliminary but offers ideas for developing fully Bayesian fMRI models, incorporating a plausible space and time dependence structure.


Bayesian factor analysis Gaussian processes Low-rank factorizations Separable models 



We are grateful to Greg Kiar and Eric Bridgeford from NeuroData at Johns Hopkins University, who graciously pre-processed the raw DTI and R-fMRI imaging data available at, using the pipelines ndmg and c-pac. The authors are also thankful to the organizers of StartUp Research for coordinating such a stimulating event.

Supplementary material


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Alessia Caponera
    • 1
  • Francesco Denti
    • 2
  • Tommaso Rigon
    • 3
    Email author
  • Andrea Sottosanti
    • 4
  • Alan Gelfand
    • 5
  1. 1.Department of Statistical SciencesSapienza University of RomeRomeItaly
  2. 2.Department of Statistics and Quantitative MethodsUniversity of Milano-BicoccaMilanItaly
  3. 3.Department of Decision SciencesBocconi UniversityMilanItaly
  4. 4.Department of Statistical SciencesUniversity of PadovaPaduaItaly
  5. 5.Department of Statistical ScienceDuke UniversityDurhamUSA

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