The Annals of Applied Statistics

A nonstationary nonparametric Bayesian approach to dynamically modeling effective connectivity in functional magnetic resonance imaging experiments

Sourabh Bhattacharya and Ranjan Maitra

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Abstract

Effective connectivity analysis provides an understanding of the functional organization of the brain by studying how activated regions influence one other. We propose a nonparametric Bayesian approach to model effective connectivity assuming a dynamic nonstationary neuronal system. Our approach uses the Dirichlet process to specify an appropriate (most plausible according to our prior beliefs) dynamic model as the “expectation” of a set of plausible models upon which we assign a probability distribution. This addresses model uncertainty associated with dynamic effective connectivity. We derive a Gibbs sampling approach to sample from the joint (and marginal) posterior distributions of the unknowns. Results on simulation experiments demonstrate our model to be flexible and a better candidate in many situations. We also used our approach to analyzing functional Magnetic Resonance Imaging (fMRI) data on a Stroop task: our analysis provided new insight into the mechanism by which an individual brain distinguishes and learns about shapes of objects.

Article information

Source
Ann. Appl. Stat., Volume 5, Number 2B (2011), 1183-1206.

Dates
First available in Project Euclid: 13 July 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1310562718

Digital Object Identifier
doi:10.1214/11-AOAS470

Mathematical Reviews number (MathSciNet)
MR2849771

Zentralblatt MATH identifier
1223.62011

Keywords
Attentional control network Bayesian analysis Dirichlet process effective connectivity analysis fMRI Gibbs sampling temporal correlation

Citation

Bhattacharya, Sourabh; Maitra, Ranjan. A nonstationary nonparametric Bayesian approach to dynamically modeling effective connectivity in functional magnetic resonance imaging experiments. Ann. Appl. Stat. 5 (2011), no. 2B, 1183--1206. doi:10.1214/11-AOAS470. https://projecteuclid.org/euclid.aoas/1310562718


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Supplemental materials

  • Supplementary material: Contents. Section S-1 contains additional details regarding our methodology, including explicit forms of the full conditional distributions of specific parameters, the configuration indicators and the distinct parameters associated with the Dirichlet process needed for Gibbs sampling. Detailed arguments that show model averaging associated with our DP-based model M_DP are also presented there. Section S-2 provides additional information on our simulation experiments, including associated methodology and results. Section S-3 presents further details on the analysis of the Stroop task experiment, including display of the data, detailed assessment of convergence of our MCMC samplers when using M_DP and M_DP^(1) and MCMC-based posterior analysis using M_AR and other additional models obtained by setting some effective connectivity parameters to zero. Additional methodological details and results regarding the smoothing of the modeled BOLD signal x(⋅) are also presented there.
    Digital Object Identifier: doi:10.1214/11-AOAS470SUPP
    Supplemental PDF (7012 KB)

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