Covariance Selection

Dempster, A. P.

doi:10.2307/2528966

Cited by 1,000 publications

(940 citation statements)

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“…In order to tackle the aforementioned issues, we developed a Bayesian framework for inferring functional connectivity which does not rely on shrinkage but rather assumes that the sparseness structure G of Ω is given (Dempster, 1972). Specifically, we assume that the graph G is given by the structural connectivity as estimated from DWI data.…”

Section: Bayesian Functional Connectivity Estimationmentioning

confidence: 99%

Structurally-informed Bayesian functional connectivity analysis

et al. 2014

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Functional connectivity refers to covarying activity between spatially segregated brain regions and can be studied by measuring correlation between functional magnetic resonance imaging (fMRI) timeseries. These correlations can be caused either by direct communication via active axonal pathways or indirectly via the interaction with other regions. It is not possible to discriminate between these two kinds of functional interaction simply by considering the covariance matrix. However, the non-diagonal elements of its inverse, the precision matrix, can be naturally related to direct communication between brain areas and interpreted in terms of partial correlations. In this paper, we propose a Bayesian model for functional connectivity analysis which allows estimation of a posterior density over precision matrices, and, consequently, allows one to quantify the uncertainty about estimated partial correlations. In order to make model estimation feasible it is assumed that the sparseness structure of the precision matrices is given by an estimate of structural connectivity obtained using diffusion imaging data. The model was tested on simulated data as well as resting-state fMRI data and compared with a graphical lasso analysis. The presented approach provides a theoretically solid foundation for quantifying functional connectivity in the presence of uncertainty.

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Section: Bayesian Functional Connectivity Estimationmentioning

confidence: 99%

Structurally-informed Bayesian functional connectivity analysis

et al. 2014

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“…In our setup, the sparsity structure is readily available in the form of structural connectivity A. In order to use A as a constraint when estimatingQ, we can make use of the fact that variables y i and y j are conditionally independent if and only if q ij = 0 (Dempster, 1972). That is, we can interpret Eq.…”

Section: Validation Of Structural Connectivity Estimatesmentioning

confidence: 99%

Bayesian inference of structural brain networks

et al. 2013

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Structural brain networks are used to model white-matter connectivity between spatially segregated brain regions. The presence, location and orientation of these white matter tracts can be derived using diffusion-weighted magnetic resonance imaging in combination with probabilistic tractography. Unfortunately, as of yet, none of the existing approaches provide an undisputed way of inferring brain networks from the streamline distributions which tractography produces. Stateof-the-art methods rely on an arbitrary threshold or, alternatively, yield weighted results that are difficult to interpret. In this paper, we provide a generative model that explicitly describes how structural brain networks lead to observed streamline distributions. This allows us to draw principled conclusions about brain networks, which we validate using simultaneously acquired resting-state functional MRI data. Inference may be further informed by means of a prior which combines connectivity estimates from multiple subjects. Based on this prior, we obtain networks that significantly improve on the conventional approach.

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“…Primal contributions to the methodology are due to Dempster (1972) and Darroch et al (1980). DAGs and CIGs imply a different definition of joint probability.…”

Section: Graphical Modellingmentioning

confidence: 99%

Identification of monetary policy in SVAR models: a data-oriented perspective

Fragetta

Melina

2012

Empir Econ

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This is the unspecified version of the paper.This version of the publication may differ from the final published version. Permanent AbstractIn the literature using short-run timing restrictions to identify monetary policy shocks in vector-autoregressions (VAR) there is a debate on whether (i) contemporaneous real activity and prices or (ii) only data typically observed with high frequency should be assumed to be in the information set of the central bank when the interest rate decision is taken. This paper applies graphical modelling theory, a data-based tool, in a small-scale VAR of the US economy to shed light on this issue. Results corroborate the second type of assumption.

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Covariance Selection

Cited by 1,000 publications

References 0 publications

Structurally-informed Bayesian functional connectivity analysis

Structurally-informed Bayesian functional connectivity analysis

Bayesian inference of structural brain networks

Identification of monetary policy in SVAR models: a data-oriented perspective

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