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.
BFDA: A Matlab Toolbox for Bayesian Functional Data Analysis
We provide a MATLAB toolbox, BFDA, that implements a Bayesian hierarchical model to smooth multiple functional data with the assumptions of the same underlying Gaussian process distribution, a Gaussian process prior for the mean function, and an Inverse-Wishart process prior for the covariance function . This model-based approach can borrow strength from all functional data to increase the smoothing accuracy, as well as estimate the mean- covariance functions simultaneously. An option of approximating the Bayesian inference process using cubic B-spline basis functions is integrated in BFDA, wh…
Nonparametric Correlation Estimator via Solving Cubic Equations and its Application to Brain Functional Connectivity Analysis
Lijiang Culture and Tourism College（丽江文化旅游学院）；York Neuroimaging Centre, University of York（约克大学神经影像中心）；School of Mathematics, Statistics and Actuarial Science, University of Kent（肯特大学数学、统计与精算科学学院）
Bayesian Varying-Effects Vector Autoregressive Models for Inference of Brain Connectivity Networks and Covariate Effects in Pediatric Traumatic Brain Injury
Smoothing and mean-covariance estimation of functional data with a Bayesian hierarchical model
Functional data, with basic observational units being functions (e.g., curves, surfaces) varying over a continuum, are frequently encountered in various applications. While many statistical tools have been developed for functional data analysis, the issue of smoothing all functional observations simultaneously is less studied. Existing methods often focus on smoothing each individual function separately, at the risk of removing important systematic patterns common across functions. We propose a nonparametric Bayesian approach to smooth all functional observations simultaneously and nonparametr…
CITS: Nonparametric Statistical Causal Modeling for High-Resolution Neural Time Series
University of California, San Francisco（旧金山加利福尼亚大学）；UCSF Weill Institute for Neurosciences（旧金山加利福尼亚大学威尔神经科学研究所）；Center for Research on Science and Consciousness（科学与意识研究中心）；National University of Singapore（新加坡国立大学）；Department of Bioengineering and Therapeutic Sciences, University of California, San Francisco（旧金山加利福尼亚大学生物工程与治疗科学系）
Topological Effective Connectivity Modeling in Brain Networks
King Abdullah University of Science Technology（阿卜杜拉国王科技大学）；Department of Statistics, University of Wisconsin-Madison（威斯康星大学麦迪逊分校统计系）；Statistics Program, King Abdullah University of Science and Technology（阿卜杜拉国王科技大学统计学项目）
