Bayesian Population Modeling of Effective Connectivity

A hierarchical model based on the Multivariate Autoregessive (MAR) process is proposed to jointly model neurological time-series collected from multiple subjects, and to characterize the distribution of MAR coefficients across the population from which those subjects were drawn. Thus, inference about effective connectivity between brain regions may be generalized beyond those subjects studied. The posterior on population- and subject-level connectivity parameters are estimated in a Variational Bayesian (VB) framework, and structural model parameters are chosen by the corresponding evidence criteria. The significance of resulting connectivity statistics are evaluated by permutation-based approximations to the null distribution. The method is demonstrated on simulated data and on actual multi-subject neurological time-series.

[1]  F. Gonzalez-Lima,et al.  Structural equation modeling and its application to network analysis in functional brain imaging , 1994 .

[2]  H. Begleiter,et al.  Event related potentials during object recognition tasks , 1995, Brain Research Bulletin.

[3]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[4]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[5]  S. Roberts,et al.  Bayesian multivariate autoregressive models with structured priors , 2002 .

[6]  A. Gelman.  Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) , 2004 .

[7]  Geoffrey E. Hinton,et al.  Keeping the neural networks simple by minimizing the description length of the weights , 1993, COLT '93.

[8]  Mingzhou Ding,et al.  Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance , 2001, Biological Cybernetics.

[9]  William H. Press,et al.  Numerical recipes in C , 2002 .

[10]  Karl J. Friston,et al.  Dynamic causal modelling , 2003, NeuroImage.

[11]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[12]  A. R. McIntosh,et al.  The Application of Structural Modeling to Metabolic Mapping of Functional Neural Systems , 1992 .

[13]  Xiao-Li Meng,et al.  Fast EM‐type implementations for mixed effects models , 1998 .

[14]  David J. C. MacKay,et al.  BAYESIAN NON-LINEAR MODELING FOR THE PREDICTION COMPETITION , 1996 .

[15]  Nikunj C. Oza,et al.  Online Ensemble Learning , 2000, AAAI/IAAI.

[16]  Karl J. Friston,et al.  Classical and Bayesian Inference in Neuroimaging: Theory , 2002, NeuroImage.

[17]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics , 2019, Wiley Series in Probability and Statistics.

[18]  Karl J. Friston,et al.  Multivariate Autoregressive Modelling of fMRI time series , 2003 .