Citation Context

...he accuracy with the number of modes (left bar graph) but in the context of increasing model complexity (right bar graph). The complexity is just the difference between the free energy and accuracy. (=-=Kass and Raftery, 1995-=-)), one could consider Bayesian averaging over models (Penny et al., 2010); such that the posterior expectations are weighted by the respective evidence for their model. However, in our case, the winn...

Citation Context

...tersen, 1998; Price, 2000). The second contrast was “fixation>all tasks” and identified four task-induced deactivations that are part of the well-known default mode network (Greicius and Menon, 2004; =-=Raichle et al., 2001-=-)—including bilateral inferior parietal lobule, posterior cingulate cortex and medial prefrontal cortex (Fig. 1). Our rationale – of selecting nodes with both task-induced activations and deactivation...

Citation Context

...or random fluctuations (Valdes-Sosa et al., 2011). Recently, there has been growing interest in the modelling of larger networks or graphs, which we take to imply graphs with sixteen or more regions (=-=Bullmore and Sporns, 2009-=-; Guye et al., 2010; He and Evans, 2010). These analyses are usually required to contextualise the activity in subgraphs, within the setting of a larger distributed network—or to provide estimates of ...

Citation Context

...vity beyond the subgraphs normally examined in DCM. © 2012 Elsevier Inc. All rights reserved. Introduction Usually, analyses of directed (effective) connectivity using dynamic causal modelling (DCM) (=-=Friston et al., 2003-=-) on fMRI data consider a small number of regions (e.g., less than 10 regions), typically excited by carefully designed experimental manipulations (for a review see (Friston, 2011b; Seghier et al., 20...

Citation Context

...network—or to provide estimates of effective connectivity for subsequent characterisation with graph theory measures such as characteristic path length, modularity, centrality and network resilience (=-=Rubinov and Sporns, 2010-=-). However, increasing the number of regions or nodes in a DCM presents some problems. Clearly, the number of extrinsic (between-node) connections or edges increases with the square of the number of n...

Citation Context

...ctor θ. The posterior probabilities of the model parameters θ=(A,B,C,H) are assessed with Bayesian inversion using standard variational techniques based upon the Laplace approximation (Friston, 2002; =-=Friston et al., 2002-=-, 2007a). In this Bayesian inversion framework, two quantities are estimated (e.g. (Daunizeau et al., 2011)): (i) the posterior distribution over model parameters p(θ|M,Y), which can be used to ð1Þ ma...

Citation Context

...uted brain responses are mediated by coupling among spatial patterns or modes (Friston, 2009), of the sort seen in resting state functional connectivity studies; see for example (Biswal et al., 2010; =-=Damoiseaux et al., 2006-=-; Smith et al., 2009; Yeo et al., 2011). This means that the connections among individual regions can be replaced by connections among modes. Because we can control the number of modes, one can place ...

Citation Context

...mediated by coupling among spatial patterns or modes (Friston, 2009), of the sort seen in resting state functional connectivity studies; see for example (Biswal et al., 2010; Damoiseaux et al., 2006; =-=Smith et al., 2009-=-; Yeo et al., 2011). This means that the connections among individual regions can be replaced by connections among modes. Because we can control the number of modes, one can place an upper bound on th...

Citation Context

...pothesis that distributed brain responses are mediated by coupling among spatial patterns or modes (Friston, 2009), of the sort seen in resting state functional connectivity studies; see for example (=-=Biswal et al., 2010-=-; Damoiseaux et al., 2006; Smith et al., 2009; Yeo et al., 2011). This means that the connections among individual regions can be replaced by connections among modes. Because we can control the number...

Citation Context

...ution is based on plausible priors that effectively constrain the number of extrinsic coupling parameters. Crucially, the plausibility of these priors can be established by Bayesian model comparison (=-=Penny et al., 2004-=-, 2010). This approach is based upon the hypothesis that distributed brain responses are mediated by coupling among spatial patterns or modes (Friston, 2009), of the sort seen in resting state functio...

Citation Context

... region can still have its own hemodynamic response function. It is also worth noting that priors on the noise precision at each node remain independent (for more details see (Daunizeau et al., 2009; =-=Friston et al., 2007a-=-; Li et al., 2011)). Note that the use of modes – as prior constraints on coupling among nodes – is similar to but formally distinct from modelling the coupling among modes per se; e.g. (Stevens et al...

Citation Context

... cortex and anterior cingulate (BA 10/24) −2 40 −10 activations during reading aloud relative to fixation – including a large bilateral set of visual, auditory, phonological and articulatory regions (=-=Fiez and Petersen, 1998-=-; Price, 2000). The second contrast was “fixation>all tasks” and identified four task-induced deactivations that are part of the well-known default mode network (Greicius and Menon, 2004; Raichle et a...

Citation Context

...mbedding as detailed in Friston et al., 2011). This revealed for instance a difference in the strength of bidirectional coupling between the core midline regions of the default mode network (as hubs (=-=Andrews-Hanna et al., 2010-=-)), with the other nodes of the reading system (see nodes 19 and 20 of Fig. 6C). We will not comment further on this connectivity graph; however, many readers will note that the underlying weighted ad...

Citation Context

...are noted as vector θ. The posterior probabilities of the model parameters θ=(A,B,C,H) are assessed with Bayesian inversion using standard variational techniques based upon the Laplace approximation (=-=Friston, 2002-=-; Friston et al., 2002, 2007a). In this Bayesian inversion framework, two quantities are estimated (e.g. (Daunizeau et al., 2011)): (i) the posterior distribution over model parameters p(θ|M,Y), which...

Citation Context

...11). Recently, there has been growing interest in the modelling of larger networks or graphs, which we take to imply graphs with sixteen or more regions (Bullmore and Sporns, 2009; Guye et al., 2010; =-=He and Evans, 2010-=-). These analyses are usually required to contextualise the activity in subgraphs, within the setting of a larger distributed network—or to provide estimates of effective connectivity for subsequent c...

Citation Context

...elling (DCM) (Friston et al., 2003) on fMRI data consider a small number of regions (e.g., less than 10 regions), typically excited by carefully designed experimental manipulations (for a review see (=-=Friston, 2011b-=-; Seghier et al., 2010b)). In terms of graph theory, this corresponds to a characterisation of subgraphs that are exposed to exogenous input—where these inputs can be experimental (stimulus) functions...

Citation Context

...distributed processing. The selection of candidate nodes for subsequent DCM analysis is generally motivated by one of two aims: network discovery through structural model selection (see discussion in =-=Roebroeck et al., 2011-=-) or testing hypotheses about specific connections. In the latter context,190 M.L. Seghier, K.J. Friston / NeuroImage 68 (2013) 181–191 inferences on models with a small number of nodes are generally...

Citation Context

...Fax: +44 20 7813 1420. E-mail address: m.seghier@ucl.ac.uk (M.L. Seghier). This can lead to models with enormous numbers of free parameters and profound conditional dependencies among the parameters (=-=Daunizeau et al., 2011-=-). Furthermore, the computational time required to invert these models grows exponentially with the number of free parameters. In this paper, we present a simple solution to the inversion of large DCM...

Citation Context

.... In terms of graph theory, this corresponds to a characterisation of subgraphs that are exposed to exogenous input—where these inputs can be experimental (stimulus) functions or random fluctuations (=-=Valdes-Sosa et al., 2011-=-). Recently, there has been growing interest in the modelling of larger networks or graphs, which we take to imply graphs with sixteen or more regions (Bullmore and Sporns, 2009; Guye et al., 2010; He...

Citation Context

...ncreasing model complexity (right bar graph). The complexity is just the difference between the free energy and accuracy. (Kass and Raftery, 1995)), one could consider Bayesian averaging over models (=-=Penny et al., 2010-=-); such that the posterior expectations are weighted by the respective evidence for their model. However, in our case, the winning model had a sufficiently high log evidence to make this Bayesian para...

Citation Context

... unchanged and thus each region can still have its own hemodynamic response function. It is also worth noting that priors on the noise precision at each node remain independent (for more details see (=-=Daunizeau et al., 2009-=-; Friston et al., 2007a; Li et al., 2011)). Note that the use of modes – as prior constraints on coupling among nodes – is similar to but formally distinct from modelling the coupling among modes per ...

Citation Context

...ablished by Bayesian model comparison (Penny et al., 2004, 2010). This approach is based upon the hypothesis that distributed brain responses are mediated by coupling among spatial patterns or modes (=-=Friston, 2009-=-), of the sort seen in resting state functional connectivity studies; see for example (Biswal et al., 2010; Damoiseaux et al., 2006; Smith et al., 2009; Yeo et al., 2011). This means that the connecti...

Citation Context

...ive and negative posterior estimates of the coupling parameters and to explicitly model interactions between functionally heterogeneous networks (e.g. (AndrewsHanna et al., 2010; Graves et al., 2010; =-=Laird et al., 2009-=-; Richardson et al., 2011; Seghier and Price, 2009; Seghier et al., 2010a; Wirth et al., 2011)). After defining our 20 regions from the group analysis, principal eigenvariates (i.e., summary time seri...

Citation Context

...s on models with a small number of nodes are generally sufficient, given that conditional estimates of effective connectivity from a full graph are often consistent with estimates based on subgraphs (=-=Friston, 2011a-=-). In the setting of network discovery, our approach enables the inversion of large DCMs that can then be submitted to graph theory and related analyses. In principle, the analyses described in this p...

Citation Context

...des-Sosa et al., 2011). Recently, there has been growing interest in the modelling of larger networks or graphs, which we take to imply graphs with sixteen or more regions (Bullmore and Sporns, 2009; =-=Guye et al., 2010-=-; He and Evans, 2010). These analyses are usually required to contextualise the activity in subgraphs, within the setting of a larger distributed network—or to provide estimates of effective connectiv...

Citation Context

... explicitly model interactions between functionally heterogeneous networks (e.g. (AndrewsHanna et al., 2010; Graves et al., 2010; Laird et al., 2009; Richardson et al., 2011; Seghier and Price, 2009; =-=Seghier et al., 2010a-=-; Wirth et al., 2011)). After defining our 20 regions from the group analysis, principal eigenvariates (i.e., summary time series) were extracted from each subject (using voxels in subject-specific SP...

Citation Context

...et al., 2007a; Li et al., 2011)). Note that the use of modes – as prior constraints on coupling among nodes – is similar to but formally distinct from modelling the coupling among modes per se; e.g. (=-=Stevens et al., 2007-=-)). In other words, the DCM is still trying to explain region-specific activity in each node (as opposed to the activity of modes). This concludes our description of how functionally informed modes of...

Citation Context

...model p(Y|M), known as the model evidence or marginal likelihood. The log evidence is approximated by a negative (variational) free energy that is used for Bayesian model comparison or scoring (e.g. (=-=Penny, 2012-=-)). Further details about DCM for fMRI responses can be found elsewhere (Friston, 2011b; Seghier et al., 2010b). Priors on the parameters of DCM for fMRI In this work, we used the latest release of DC...

Citation Context

...its own hemodynamic response function. It is also worth noting that priors on the noise precision at each node remain independent (for more details see (Daunizeau et al., 2009; Friston et al., 2007a; =-=Li et al., 2011-=-)). Note that the use of modes – as prior constraints on coupling among nodes – is similar to but formally distinct from modelling the coupling among modes per se; e.g. (Stevens et al., 2007)). In oth...

Citation Context

...ber of a priori modes) could be applied to any fMRI time series using DCMs with full extrinsic connectivity. The model with the greatest evidence can then be pruned using post-hoc model optimisation (=-=Friston et al., 2011-=-) to provide posterior estimates for subsequent characterisation of the resulting directed graphs. We will illustrate these procedures using empirical data. This paper comprises three sections. In the...

Citation Context

...iston et al., 2003) on fMRI data consider a small number of regions (e.g., less than 10 regions), typically excited by carefully designed experimental manipulations (for a review see (Friston, 2011b; =-=Seghier et al., 2010b-=-)). In terms of graph theory, this corresponds to a characterisation of subgraphs that are exposed to exogenous input—where these inputs can be experimental (stimulus) functions or random fluctuations...

Citation Context

.... Interestingly, this is exactly the same as the use of (undirected probabilistic) anatomical connectivity, when using diffusion weighted imaging or tractography data to inform dynamic causal models (=-=Stephan et al., 2009-=-). The use of such informative constraints ensures that each node still has its own intrinsic connectivity and haemodynamic parameters, while enabling DCM to provide unbiased and more efficient estima...

Citation Context

... intensive. This means the search for the optimal number of prior covariance (functional connectivity) modes may become prohibitive. However, this problem can be finessed using post-hoc optimisation (=-=Friston and Penny, 2011-=-). In other words, one would invert a full model (with no covariance constraints) and then evaluate the post-hoc model evidence (free energy) of reduced models, whose prior covariances have progressiv...

Citation Context

...– was to ensure positive and negative posterior estimates of the coupling parameters and to explicitly model interactions between functionally heterogeneous networks (e.g. (AndrewsHanna et al., 2010; =-=Graves et al., 2010-=-; Laird et al., 2009; Richardson et al., 2011; Seghier and Price, 2009; Seghier et al., 2010a; Wirth et al., 2011)). After defining our 20 regions from the group analysis, principal eigenvariates (i.e...

Citation Context

...oupling parameters and to explicitly model interactions between functionally heterogeneous networks (e.g. (AndrewsHanna et al., 2010; Graves et al., 2010; Laird et al., 2009; Richardson et al., 2011; =-=Seghier and Price, 2009-=-; Seghier et al., 2010a; Wirth et al., 2011)). After defining our 20 regions from the group analysis, principal eigenvariates (i.e., summary time series) were extracted from each subject (using voxels...

Citation Context

...the selection of regions or nodes and the ensuing dynamic causal model. The empirical data came from a block-design fMRI activation study of 10 healthy subjects described in (Seghier and Price, 2010; =-=Seghier et al., 2008-=-). During two separate scanning sessions, subjects were asked to (i) read aloud 96 three to six letter object names with consistent spelling-to-sound relationships (e.g. hat, tent, horse, carrot); (ii...

Citation Context

...terior estimates of the coupling parameters and to explicitly model interactions between functionally heterogeneous networks (e.g. (AndrewsHanna et al., 2010; Graves et al., 2010; Laird et al., 2009; =-=Richardson et al., 2011-=-; Seghier and Price, 2009; Seghier et al., 2010a; Wirth et al., 2011)). After defining our 20 regions from the group analysis, principal eigenvariates (i.e., summary time series) were extracted from e...

Citation Context

... projector, a front-projection screen and a system of mirrors attached to a head coil. Additional details about the paradigm and stimuli can be found in our previous descriptions of this study (c.f. (=-=Kherif et al., 2009-=-; Seghier and Price, 2010; Seghier et al., 2008)). fMRI data acquisition and analysis Data were acquired on a 1.5 T scanner (Siemens Medical Systems, Erlangen, Germany). Functional imaging consisted o...

Citation Context

...ecent trends of using informed or tailored priors based on prior beliefs forwarded by models of anatomical connectivity—or on the basis of meta-analytic functional connectivity (see recent review in (=-=Fox and Friston, 2012-=-)). Future work needs to explore how our findings generalise to other DCM schemes, including stochastic DCM (Daunizeau et al., 2009; Li et al., 2011). Acknowledgments This work was funded by the Welco...

Citation Context

...the experimental design, the selection of regions or nodes and the ensuing dynamic causal model. The empirical data came from a block-design fMRI activation study of 10 healthy subjects described in (=-=Seghier and Price, 2010-=-; Seghier et al., 2008). During two separate scanning sessions, subjects were asked to (i) read aloud 96 three to six letter object names with consistent spelling-to-sound relationships (e.g. hat, ten...

Citation Context

...actions between functionally heterogeneous networks (e.g. (AndrewsHanna et al., 2010; Graves et al., 2010; Laird et al., 2009; Richardson et al., 2011; Seghier and Price, 2009; Seghier et al., 2010a; =-=Wirth et al., 2011-=-)). After defining our 20 regions from the group analysis, principal eigenvariates (i.e., summary time series) were extracted from each subject (using voxels in subject-specific SPMs that survived a c...